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Complexity of sparse polynomial solving 2: renormalization IMA J. Numer. Anal. (IF 2.713) Pub Date : 20221003
Gregorio MalajovichRenormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length, defined as a line integral of the condition number along all the lifted renormalized paths. The theory developed in this paper leads to a continuation algorithm tracking

Recovery of a spacetimedependent diffusion coefficient in subdiffusion: stability, approximation and error analysis IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220927
Bangti Jin, Zhi ZhouIn this work we study an inverse problem of recovering a spacetimedependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian–Caputo fractional derivative of order $\alpha \in (0,1)$ in time. The main technical challenges of both theoretical and numerical analyses lie in the limited smoothing properties due to the

On approximation classes for adaptive timestepping finite element methods IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220916
Marcelo Actis, Pedro Morin, Cornelia SchneiderWe study approximation classes for adaptive timestepping finite element methods for timedependent partial differential equations. We measure the approximation error in $L_2([0,T)\times \varOmega )$ and consider the approximation with discontinuous finite elements in time and continuous finite elements in space, of any degree. As a byproduct we define anisotropic Besov spaces for Banachspacevalued

Smaller generalization error derived for a deep residual neural network compared with shallow networks IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220913
Aku Kammonen, Jonas Kiessling, Petr Plecháč, Mattias Sandberg, Anders Szepessy, Raul TemponeEstimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell +1}=\bar z_\ell + \textrm {Re}\sum _{k=1}^K\bar b_{\ell k}\,e^{\textrm {i}\omega _{\ell k}\bar z_\ell }+ \textrm {Re}\sum _{k=1}^K\bar c_{\ell k}\,e^{\textrm {i}\omega ^{\prime}_{\ell k}\cdot x}$. An optimal distribution for the frequencies $(\omega _{\ell k},\omega ^{\prime}_{\ell

Padéparametric FEM approximation for fractional powers of elliptic operators on manifolds IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220907
Beiping DuanThis paper focuses on numerical approximation for fractional powers of elliptic operators on twodimensional manifolds. Firstly, the parametric finite element method is employed to discretize the original problem. We then approximate fractional powers of the discrete elliptic operator by the product of rational functions, each of which is a diagonal Padé approximant for the corresponding power function

An analysis of the steepest descent method to efficiently compute the threedimensional acoustic singlelayer operator in the highfrequency regime IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220831
D Gasperini, H P Beise, U Schroeder, X Antoine, C GeuzaineUsing the Cauchy integral theorem, we develop the application of the steepest descent method to efficiently compute the threedimensional acoustic singlelayer integral operator for large wave numbers. Explicit formulas for the splitting points are derived in the onedimensional case to build suitable complex integration paths. The construction of admissible steepest descent paths is next investigated

The MHM Method for Linear Elasticity on Polytopal Meshes IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220824
Antônio Tadeu A Gomes, Weslley S Pereira, Frédéric ValentinThe multiscale hybridmixed (MHM) method consists of a multilevel strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a new family of finite elements for the linear elasticity equation defined on coarse polytopal partitions of the domain. The finite elements rely on face degrees of freedom associated with multiscale bases obtained

Optimal rates of convergence and error localization of Gegenbauer projections IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220824
Haiyong WangMotivated by comparing the convergence behavior of Gegenbauer projections and best approximations, we study the optimal rate of convergence for Gegenbauer projections in the maximum norm. We show that the rate of convergence of Gegenbauer projections is the same as that of best approximations under conditions of the underlying function being either analytic on and within an ellipse and $\lambda \leqslant

Mixed precision lowrank approximations and their application to block lowrank LU factorization IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220824
Patrick Amestoy, Olivier Boiteau, Alfredo Buttari, Matthieu Gerest, Fabienne Jézéquel, JeanYves L’Excellent, Theo MaryWe introduce a novel approach to exploit mixed precision arithmetic for lowrank approximations. Our approach is based on the observation that singular vectors associated with small singular values can be stored in lower precisions while preserving high accuracy overall. We provide an explicit criterion to determine which level of precision is needed for each singular vector. We apply this approach

Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220824
Balázs Kovács, Buyang LiMaximal parabolic $L^p$regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations

Inexact NewtonCG algorithms with complexity guarantees IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220823
Zhewei Yao, Peng Xu, Fred Roosta, Stephen J Wright, Michael W MahoneyWe consider variants of a recently developed NewtonCG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of secondorder linesearch algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures

An asymptoticpreserving discretization scheme for gas transport in pipe networks IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220820
H Egger, J Giesselmann, T Kunkel, N PhilippiWe consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and an implicit Euler method in time. Assuming the existence of a smooth subsonic solution bounded away from vacuum, a full convergence analysis is presented based on

Multilevel representations of isotropic Gaussian random fields on the sphere IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220820
Markus Bachmayr, Ana DjurdjevacSeries expansions of isotropic Gaussian random fields on $\mathbb {S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localized structure provide an alternative to the standard Karhunen–Loève expansions of isotropic random fields in terms of spherical harmonics. The basis functions are obtained by applying the square root

Analysis of a mixed discontinuous Galerkin method for the timeharmonic Maxwell equations with minimal smoothness requirements IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220820
Kaifang Liu, Dietmar Gallistl, Matthias Schlottbom, J J W van der VegtAn error analysis of a mixed discontinuous Galerkin (DG) method with lifting operators as numerical fluxes for the timeharmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that due to the low regularity the tangential trace of the exact solution is not well defined on the faces of the computational mesh. This difficulty

Numerical analysis of multiple scattering theory for electronic structure calculations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220817
Xiaoxu Li, Huajie Chen, Xingyu GaoMultiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between atomic configurations and site potentials and hence provides an efficient way to simulate defected and disordered systems. This work studies MST methods from a numerical point of view and shows convergence with respect to the truncation of the angular

Global and explicit approximation of piecewisesmooth twodimensional functions from cellaverage data IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220809
Sergio Amat, David Levin, Juan RuizAlvárez, Dionisio F YáñezGiven cellaverage data values of a piecewisesmooth bivariate function $f$ within a domain $\varOmega $, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate approximation techniques, as trigonometric or splines approximations, achieve reduced approximation orders near the boundary of the domain and near curves of jump singularities

On convergence of numerical solutions for the compressible MHD system with weakly divergencefree magnetic field IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220803
Yang Li, Bangwei SheWe study a general convergence theory for the analysis of numerical solutions to a magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension $d$$(=2,3)$. First, we introduce the concept of dissipative weak (DW) solutions and prove the weak–strong uniqueness property for DW solutions, meaning a DW solution coincides with a classical

Solvability of discrete Helmholtz equations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220803
Maximilian Bernkopf, Stefan Sauter, Céline Torres, Alexander VeitWe study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin finite element method. Wellposedness of the discrete equations is typically investigated by applying a compact perturbation argument to the continuous Helmholtz problem so that a `sufficiently rich' discretization results in a `sufficiently small' perturbation of the continuous

Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonselfadjoint problems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220802
Niall Bootland, Victorita Dolean, Ivan G Graham, Chupeng Ma, Robert ScheichlGeneralized eigenvalue problems on the overlap(GenEO) is a method for computing an operatordependent spectral coarse space to be combined with local solves on subdomains to form a robust parallel domain decomposition preconditioner for elliptic PDEs. It has previously been proved, in the selfadjoint and positivedefinite case, that this method, when used as a preconditioner for conjugate gradients

Approximation of fractional harmonic maps IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220729
Harbir Antil, Sören Bartels, Armin SchikorraThis paper addresses the approximation of fractional harmonic maps. Besides a unitlength constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unitlength vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic

A secondorder accurate numerical scheme for a timefractional Fokker–Planck equation IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220727
Kassem Mustapha, Omar M Knio, Olivier P Le MaîtreA secondorder accurate timestepping scheme for solving a timefractional Fokker–Planck equation of order $\alpha \in (0, 1)$, with a general driving force, is investigated. A stability bound for the semidiscrete solution is obtained for $\alpha \in (1/2,1)$ via a novel and concise approach. Our stability estimate is $\alpha $robust in the sense that it remains valid in the limiting case where $\alpha

Nonsmooth data error estimates of the L1 scheme for subdiffusion equations with positivetype memory term IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220718
Shantiram Mahata, Rajen Kumar SinhaThis paper considers fully discrete finite element approximations to subdiffusion equations with memory in a bounded convex polygonal domain. We first derive some regularity results for the solution with respect to both smooth and nonsmooth initial data in various Sobolev norms. These regularity estimates cover the cases when $u_0\in L^2(\varOmega )$ and the source function is Hölder continuous in

Error estimates for the numerical approximation of optimal control problems with nonsmooth pointwiseintegral control constraints IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220708
Eduardo Casas, Karl Kunisch, Mariano MateosThe numerical approximation of an optimal control problem governed by a semilinear parabolic equation and constrained by a bound on the spatial $L^1$norm of the control at every instant of time is studied. Spatial discretizations of the controls by piecewise constant and continuous piecewise linear functions are investigated. Under finite element approximations, the sparsity properties of the continuous

Fast global spectral methods for threedimensional partial differential equations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220707
Christoph Strössner, Daniel KressnerGlobal spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending the ideas of Chebop2 (Townsend, A. & Olver, S. (2015) The automatic solution of partial differential equations using a global spectral method. J. Comput

A C0 finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220702
Hengguang Li, Peimeng Yin, Zhimin ZhangIn this paper we study the biharmonic equation with Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourthorder problem as a system of Poisson equations. Our method differs from the naive mixed method that leads to two Poisson problems but only applies to convex domains; our decomposition involves a third Poisson equation to confine

A novel spectral method for the semiclassical Schrödinger equation based on the Gaussian wavepacket transform IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220426
Borui Miao, Giovanni Russo, Zhennan ZhouIn this article we develop and analyse a new spectral method to solve the semiclassical Schrödinger equation based on the Gaussian wavepacket transform (GWPT) and Hagedorn’s semiclassical wave packets. The GWPT equivalently recasts the highly oscillatory wave equation as a much less oscillatory one (the $w$ equation) coupled with a set of ordinary differential equations governing the dynamics of the

Fully discrete bestapproximationtype estimates in L∞ (I;L2(Ω)d) for finite element discretizations of the transient Stokes equations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220425
Niklas Behringer,Boris Vexler,Dmitriy LeykekhmanAbstract In this article, we obtain an optimal bestapproximationtype result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete infsup condition. The analysis uses the technique of discrete maximal parabolic

Twopoint Landwebertype method with convex penalty terms for nonsmooth nonlinear inverse problems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220422
Zhenwu Fu,Wei Wang,Bo Han,Yong ChenAbstract In this work, we propose a twopoint Landwebertype method with general convex penalty terms for solving nonsmooth nonlinear inverse problems. The design of our method can cope with nonsmooth nonlinear inverse problems or the nonlinear inverse problems whose data are contaminated by various types of noise. The method consists of the twopoint acceleration strategy and inner solvers. Inner

Effects of roundtonearest and stochastic rounding in the numerical solution of the heat equation in low precision IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220422
M Croci,M B GilesAbstract Motivated by the advent of machine learning, the last few years have seen the return of hardwaresupported lowprecision computing. Computations with fewer digits are faster and more memory and energy efficient but can be extremely susceptible to rounding errors. As shown by recent studies into reducedprecision climate simulations, an application that can largely benefit from the advantages

Accelerated exponential Euler scheme for stochastic heat equation: convergence rate of the density IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220419
Chuchu Chen,Jianbo Cui,Jialin Hong,Derui ShengAbstract This paper studies the numerical approximation of the density of the stochastic heat equation driven by spacetime white noise via the accelerated exponential Euler scheme. The existence and smoothness of the density of the numerical solution are proved by means of Malliavin calculus. Based on a priori estimates of the numerical solution we present a testfunctionindependent weak convergence

Interpolation and stability properties of loworder face and edge virtual element spaces IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220328
L Beirão da Veiga,L MascottoAbstract We analyse the interpolation properties of twodimensional and threedimensional loworder virtual element (VE) face and edge spaces, which generalize Nédélec and Raviart–Thomas polynomials to polygonalpolyhedral meshes. Moreover, we investigate the stability properties of the associated $L^2$discrete bilinear forms, which typically appear in the VE discretization of problems in electromagnetism

Adaptive regularization minimization algorithms with nonsmooth norms IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220322
S Gratton, Ph L TointAn adaptive regularization algorithm (AR$1p$GN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularization term involving a possibly nonsmooth norm. It is shown that the nonsmoothness of the norm does not affect the ${\mathcal {O}}(\epsilon _1^{(p+1)/p})$ upper bound on evaluation complexity for finding firstorder

Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220318
Robert Altmann,Balázs Kovács,Christoph ZimmerAbstract This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the

Error estimates for finite differences approximations of the total variation IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220318
Corentin Caillaud,Antonin ChambolleAbstract We present a convergence rate analysis of the Rudin–Osher–Fatemi (ROF) denoising problem for two different discretizations of the total variation. The first is the standard discretization, which induces blurring in some particular diagonal directions. We prove that in a simplified setting corresponding to such a direction, the discrete ROF energy converges to the continuous one with the rate

Numerical solution of an H (curl)elliptic hemivariational inequality IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220318
Weimin Han,Min Ling,Fei WangAbstract This paper is concerned with the analysis and numerical solution of an $\boldsymbol {H}({\textbf {curl}})$elliptic hemivariational inequality (HVI). One source of the HVI is through a temporal semidiscretization of a related hyperbolic Maxwell equation problem. An equivalent minimization principle is introduced, and the solution existence and uniqueness of the $\boldsymbol {H}({\textbf {curl}})$elliptic

Multiple projection Markov chain Monte Carlo algorithms on submanifolds IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220317
Tony Lelièvre,Gabriel Stoltz,Wei ZhangAbstract We propose new Markov chain Monte Carlo (MCMC) algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of setvalued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show

Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thinwalled structure: stability and convergence analysis IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220317
Michele Annese,Miguel A Fernández,Lucia GastaldiAbstract The numerical approximation of incompressible fluid–structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability, but at the expense of solving a computationally demanding coupled system at each time step. For the case of the coupling with immersed thinwalled solids, we introduce a class of semiimplicit coupling

Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in two dimensions IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220223
Daniele Boffi,Johnny Guzmán,Michael NeilanAbstract We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in three scenarios: piecewise linear elements on Powell–Sabin triangulations, piecewise quadratic elements on Clough–Tocher triangulations and piecewise quartics

Efficient implementation of the exact artificial boundary condition for the exterior problem of the Stokes system in three dimensions IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220223
Sun T, Zheng C.AbstractIn this paper the Stokes system in an unbounded domain is solved by the artificial boundary method. The novelty lies in an operator form of the exact DirichlettoNeumann (DtN) mapping. With the help of the Chebyshev rational approximation of the square root function, we derive a highly accurate approximate DtN mapping, which can be numerically implemented without resorting to the eigendecomposition

Convergence of the EBT method for a nonlocal model of cell proliferation with discontinuous interaction kernel IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220118
Piotr Gwiazda, Błażej Miasojedow, Jakub Skrzeczkowski, Zuzanna SzymańskaWe consider the EBT algorithm (a particle method) for the nonlocal equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel, which is not Lipschitz continuous, thus preventing the application of standard arguments. Therefore, we use the radial symmetry of the problem instead and transform it using spherical coordinates. The resulting equation has

From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation IMA J. Numer. Anal. (IF 2.713) Pub Date : 20220106
Nadiia Derevianko, Gerlind Plonka, Markus PetzWe introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform of the given equidistant signal values. We show that ESPIRA can be interpreted as a matrix pencil method (MPM) applied to Loewner matrices. These Loewner matrices

Stabilization parameter analysis of a secondorder linear numerical scheme for the nonlocal Cahn–Hilliard equation IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211229
Xiao Li, Zhonghua Qiao, Cheng WangA secondorder accurate (in time) and linear numerical scheme is proposed and analyzed for the nonlocal Cahn–Hilliard equation. The backward differentiation formula is used as the temporal discretization, while an explicit extrapolation is applied to the nonlinear term and the concave expansive term. In addition, an $O (\varDelta {t}^2)$ artificial regularization term, in the form of $A \varDelta _N

A C1virtual element method of high order for the Brinkman equations in stream function formulation with pressure recovery IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211223
David Mora, Carlos Reales, Alberth SilgadoIn this paper, we propose and analyze a $C^1$virtual element method of high order to solve the Brinkman problem formulated in terms of the stream function. The velocity is obtained as a simple postprocess from stream function and a novel strategy is written to recover the fluid pressure. We establish optimal a priori error estimates for the stream function, velocity and pressure with constants independent

Strong convergence of Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations under local Lipschitz conditions of state variables IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211223
Yun Li, Xuerong Mao, Qingshuo Song, Fuke Wu, George YinThis paper develops strong convergence of the Euler–Maruyama (EM) schemes for approximating McKean–Vlasov stochastic differential equations (SDEs). In contrast to the existing work, a novel feature is the use of a much weaker condition—local Lipschitzian in the state variable, but under uniform linear growth assumption. To obtain the desired approximation, the paper first establishes the existence

Exact and inexact Douglas–Rachford splitting methods for solving largescale sparse absolute value equations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211220
Cairong Chen, Dongmei Yu, Deren HanExact and inexact Douglas–Rachford splitting methods are developed to solve the largescale sparse absolute value equation (AVE) $Ax  x =b$, where $A\in \mathbb {R}^{n\times n}$ and $b\in \mathbb {R}^n$. The inexact method adopts a relative error tolerance and, therefore, in the inner iterative processes, the LSQR method is employed to find a qualified approximate solution of each subproblem, resulting

Numerical analysis of the LDG method for large deformations of prestrained plates IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211217
Andrea Bonito, Diane Guignard, Ricardo H Nochetto, Shuo YangA local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in Bonito et al. (2022, LDG approximation of large deformations of prestrained plates. J. Comput. Phys., 448, 110719). This paper presents a numerical analysis of this LDG method, focusing on the free boundary case. The problem consists

A discrete boundednessbyentropy method for finitevolume approximations of crossdiffusion systems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211210
Ansgar Jüngel, Antoine ZurekAn implicit Euler finitevolume scheme for general crossdiffusion systems with volumefilling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed to possess a formal gradientflow structure that yields $L^\infty $ bounds on the continuous level. Examples include the Maxwell–Stefan systems for gas mixtures

Randomized sparse grid algorithms for multivariate integration on Haar wavelet spaces IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211201
M Wnuk, M GnewuchThe deterministic sparse grid method, also known as Smolyak’s method, is a wellestablished and widely used tool to tackle multivariate approximation problems, and there is a vast literature on it. Much less is known about randomized versions of the sparse grid method. In this paper we analyze randomized sparse grid algorithms, namely randomized sparse grid quadratures for multivariate integration

On the approximation of dispersive electromagnetic eigenvalue problems in two dimensions IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211129
Martin HallaWe consider timeharmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to signchanging permittivity and/or permeability. Previously meshing rules were reported, which guarantee the convergence of finite element approximations to the related scalar source problems. Here we generalize these results to

Optimal convergence of arbitrary Lagrangian–Eulerian isoparametric finite element methods for parabolic equations in an evolving domain IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211129
Buyang Li, Yinhua Xia, Zongze YangAn optimalorder error estimate is presented for the arbitrary Lagrangian–Eulerian (ALE) finite element method for a parabolic equation in an evolving domain, using highorder isoparametric finite elements with flat simplices in the interior of the domain. The mesh velocity can be a linear approximation of a given bulk velocity field or a numerical solution of the Laplace equation with specified boundary

A line search penaltyfree SQP method for equalityconstrained optimization without Maratos effect IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211123
Zhongwen Chen, YuHong Dai, Tauyou ZhangA line search penaltyfree sequential quadratic programming method is proposed for nonlinear equalityconstrained optimization. Generally, feasible directions are used to minimize the measurement of the constraint violation in order to deal with the inconsistency in the linearized constraints while optimal directions aim to improve the measure of optimality. A basic feature of the proposed method is

Regularizing linear inverse problems under unknown nonGaussian white noise allowing repeated measurements IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211123
Bastian Harrach, Tim Jahn, Roland PotthastWe deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact righthand side is unknown and only accessible through discretized measurements corrupted by white noise with unknown arbitrary distribution. The measuring process can be repeated, which allows to reduce and estimate the measurement error through averaging. We show convergence against the true solution

On the convergence of Broyden’s method and some accelerated schemes for singular problems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211123
Florian MannelWe consider Broyden’s method and some accelerated schemes for nonlinear equations having a strongly regular singularity of first order with a onedimensional nullspace. Our two main results are as follows. First, we show that the use of a preceding Newtonlike step ensures convergence for starting points in a starlike domain with density 1. This extends the domain of convergence of these methods significantly

Pyramid transform of manifold data via subdivision operators IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211117
Wael Mattar, Nir SharonMultiscale transforms have become a key ingredient in many data processing tasks. With technological development we observe a growing demand for methods to cope with nonlinear data structures such as manifold values. In this paper we propose a multiscale approach for analyzing manifoldvalued data using a pyramid transform. The transform uses a unique class of downsampling operators that enable a noninterpolating

Improved structural methods for nonlinear differentialalgebraic equations via combinatorial relaxation IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211115
Taihei OkiDifferentialalgebraic equations (DAEs) are widely used for modelling dynamical systems. In the numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing steps prior to numerical integration. Existing DAE solvers commonly adopt structural preprocessing methods based on combinatorial optimization. Unfortunately, structural methods fail if the DAE has a singular

Estimates on the generalization error of physicsinformed neural networks for approximating PDEs IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211109
Siddhartha Mishra, Roberto MolinaroPhysicsinformed neural networks (PINNs) have recently been widely used for robust and accurate approximation of partial differential equations (PDEs). We provide upper bounds on the generalization error of PINNs approximating solutions of the forward problem for PDEs. An abstract formalism is introduced and stability properties of the underlying PDE are leveraged to derive an estimate for the generalization

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211108
Jonathan Jung, Vincent PerrierThis article is dedicated to the long time behavior of a finite volume approximation of general symmetrizable linear hyperbolic system on a bounded domain. In the continuous case this problem is very difficult, and the $\omega $–limit set (namely the set of all the possible long time limits) may be large and complicated to depict if no dissipation is introduced. In this article we prove that in general

A consistent quasi–secondorder staggered scheme for the twodimensional shallow water equations IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211105
Raphaèle Herbin, JeanClaude Latché, Youssouf Nasseri, Nicolas ThermeA quasi–secondorder scheme is developed to obtain approximate solutions of the twodimensional shallow water equations (SWEs) with bathymetry. The scheme is based on a staggered finite volume space discretization: the scalar unknowns are located in the discretization cells while the vector unknowns are located on the edges of the mesh. A monotonic upwindcentral scheme for conservation laws (MUSCL)like

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211101
Assyr Abdulle, CharlesEdouard Bréhier, Gilles VilmartExplicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper we provide a fully discrete strong convergence analysis of a family of explicit stabilized methods coupled with finite element methods for a class of parabolic semilinear deterministic

A proximal bundle algorithm for nonsmooth optimization on Riemannian manifolds IMA J. Numer. Anal. (IF 2.713) Pub Date : 20211028
Najmeh Hoseini Monjezi, Soghra Nobakhtian, Mohamad Reza PouryayevaliProximal bundle methods are among the most successful approaches for convex and nonconvex optimization problems in linear spaces and it is natural to extend these methods to the manifold setting. In this paper we propose a proximal bundle method for solving nonsmooth, nonconvex optimization problems on Riemannian manifolds. At every iteration, by using the proximal bundle method a candidate descent