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Pressure and convection robust bounds for continuous interior penalty divergencefree finite element methods for the incompressible Navier–Stokes equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240207
Bosco GarcíaArchilla, Julia NovoIn this paper, we analyze a pressurerobust method based on divergencefree mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust

An Eulerian finite element method for the linearized Navier–Stokes problem in an evolving domain IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240130
Michael Neilan, Maxim OlshanskiiThe paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier–Stokes problem in a timedependent domain. In this study, the domain’s evolution is assumed to be known and independent of the solution to the problem at hand. The numerical method employed in the study combines a standard backward differentiation formulatype timestepping procedure with

Goaloriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240129
Emmanuel Creusé, Serge Nicaise, Zuqi TangIn this work, we propose an a posteriori goaloriented error estimator for the harmonic $\textbf {A}$$\varphi $ formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of an adjoint problem associated with the initial one. For each of these two problems, a guaranteed equilibrated estimator is developed using

Cauchy data for Levin’s method IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240125
Anthony AshtonIn this paper, we describe the Cauchy data that gives rise to slowly oscillating solutions to the Levin equation. We present a general result on the existence of a unique minimizer of $\Bx\$ subject to the constraint $Ax=y$, where $A,B$ are linear, but not necessarily bounded operators on a complex Hilbert space. This result is used to obtain the solution to the Levin equation, both in the univariate

Full operator preconditioning and the accuracy of solving linear systems IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240125
Stephan Mohr, Yuji Nakatsukasa, Carolina UrzúaTorresUnless special conditions apply, the attempt to solve illconditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error and often slow convergence of an iterative solver. In many cases, such systems arise from the discretization of operator equations with a large number of discrete variables and the illconditioning is tackled by means of preconditioning

Wellposedness and error estimates for coupled systems of nonlocal conservation laws IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240120
Aekta Aggarwal, Helge Holden, Ganesh VaidyaThis article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in the convection term. A fairly general class of fluxes is being considered, where the local part of the flux can be discontinuous at infinitely many points, with possible

Corrigendum to: Adaptive FEM with quasioptimal overall cost for nonsymmetric linear elliptic PDEs IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240119
Maximilian Brunner, Michael Innerberger, Ani Miraçi, Dirk Praetorius, Julian Streitberger, Pascal HeidUnfortunately, there is a flaw in the numerical analysis of the published version [IMA J. Numer. Anal., DOI:10.1093/imanum/drad039], which is corrected here. Neither the algorithm nor the results are affected, but constants have to be adjusted.

Convergence with rates for a Riccatibased discretization of SLQ problems with SPDEs IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240119
Andreas Prohl, Yanqing WangWe consider a new discretization in space (parameter $h>0$) and time (parameter $\tau>0$) of a stochastic optimal control problem, where a quadratic functional is minimized subject to a linear stochastic heat equation with linear noise. Its construction is based on the perturbation of a generalized difference Riccati equation to approximate the related feedback law. We prove a convergence rate of almost

Gammaconvergent LDG method for large bending deformations of bilayer plates IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240119
Andrea Bonito, Ricardo H Nochetto, Shuo YangBilayer plates are slender structures made of two thin layers of different materials. They react to environmental stimuli and undergo large bending deformations with relatively small actuation. The reduced model is a constrained minimization problem for the second fundamental form, with a given spontaneous curvature that encodes material properties, subject to an isometry constraint. We design a local

Darcy’s problem coupled with the heat equation under singular forcing: analysis and discretization IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240111
Alejandro Allendes, Gilberto Campaña, Francisco Fuica, Enrique OtárolaWe study the existence of solutions for Darcy’s problem coupled with the heat equation under singular forcing; the righthand side of the heat equation corresponds to a Dirac measure. The model studied involves thermal diffusion and viscosity depending on the temperature. We propose a finite element solution technique and analyze its convergence properties. In the case where thermal diffusion is independent

Compactness estimates for difference schemes for conservation laws with discontinuous flux IMA J. Numer. Anal. (IF 2.1) Pub Date : 20240104
Kenneth H Karlsen, John D TowersWe establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t)$ is $BV$regular and may exhibit discontinuities along curves in the $(x,t)$ plane. Our approach, which is technically elementary, relies on a discrete interaction estimate and one entropy function

A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231223
Xiaoyin Hu, Nachuan Xiao, Xin Liu, KimChuan TohThis paper focuses on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle proxfriendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same firstorder stationary points and local minimizers as the original problem in a neighborhood of the Stiefel

On best pnorm approximation of discrete data by polynomials IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231209
Michael S FloaterIn this note, we derive a solution to the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. Analogous to a result of de la Vallée Poussin, one can express the solution as a convex combination of the Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.

Semilinear optimal control with Dirac measures IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231129
Enrique OtárolaThe purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such singular sources. We analyze the existence of optimal solutions and derive first and, necessary and sufficient, secondorder optimality conditions. We develop

Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231125
Julien CoatlévenWe derive new multiple point flux approximations (MPFA) for the finite volume approximation of heterogeneous and anisotropic diffusion problems on general meshes, in dimensions 2 and 3. The resulting methods are unconditionally stable while preserving the small stencil typical of MPFA finite volumes. The key idea is to solve local variational problems with a welldesigned stabilization term from which

Adaptive VEM for variable data: convergence and optimality IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231116
L Beirão da Veiga, C Canuto, R H Nochetto, G Vacca, M VeraniWe design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilizationfree a posteriori error estimators recently derived in Beirão da Veiga et al. (2023, Adaptive VEM: stabilizationfree a posteriori error analysis and contraction property. SIAM J. Numer. Anal., 61, 457–494). The crucial

Convergent finite element methods for the perfect conductivity problem with closetotouching inclusions IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231114
Buyang Li, Haigang Li, Zongze YangIn the perfect conductivity problem (i.e., the conductivity problem with perfectly conducting inclusions), the gradient of the electric field is often very large in a narrow region between two inclusions and blows up as the distance between the inclusions tends to zero. The rigorous error analysis for the computation of such perfect conductivity problems with closetotouching inclusions of general

A twodimensional boundary value problem of elliptic type with nonlocal conjugation conditions IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231114
Zorica Milovanović Jeknić, Aleksandra Delić, Sandra ŽivanovićWe consider an elliptic boundary value problem with nonlocal conjugation conditions. An a priori estimate for its weak solution in an appropriate Sobolevlike space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data, is obtained.

Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn–Hilliard problem IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231111
Keegan L A Kirk, Beatrice Riviere, Rami MasriThe mixed form of the Cahn–Hilliard equations is discretized by the hybridized discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the numerical solution is obtained. The scheme is proved to be unconditionally stable. Convergence of the method is obtained by deriving a priori error estimates that are valid for the Ginzburg–Landau chemical energy density and for

Twoscale methods for the normalized infinity Laplacian: rates of convergence IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231111
Wenbo Li, Abner J SalgadoWe propose a monotone and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized infinity Laplacian, which could be related to the family of the socalled twoscale methods. We show that this method is convergent and prove rates of convergence. These rates depend not only on the regularity of the solution, but also on whether or not the righthand side vanishes

Weak error analysis for strong approximation schemes of SDEs with superlinear coefficients IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231111
Xiaojie Wang, Yuying Zhao, Zhongqiang ZhangWe present an error analysis of weak convergence of onestep numerical schemes for stochastic differential equations (SDEs) with superlinearly growing coefficients. Following Milstein’s weak error analysis on the onestep approximation of SDEs, we prove a general result on weak convergence of the onestep discretization of the SDEs mentioned above. As applications, we show the weak convergence rates

Uniform L∞bounds for energyconserving higherorder time integrators for the Gross–Pitaevskii equation with rotation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231107
Christian Döding, Patrick HenningIn this paper, we consider an energyconserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed by O. Karakashian and C. Makridakis (SIAM J. Numer. Anal., 36(6)

Convergent evolving finite element approximations of boundary evolution under shape gradient flow IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231030
Wei Gong, Buyang Li, Qiqi RaoAs a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constraint partial differential equations could be solved by finite element methods on a domain with a solutiondriven evolving boundary. Rigorous analysis for the stability and convergence of such finite element

Homogeneous multigrid for HDG applied to the Stokes equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231024
Peipei Lu, Wei Wang, Guido Kanschat, Andreas RuppWe propose a multigrid method to solve the linear system of equations arising from a hybrid discontinuous Galerkin (in particular, a single face hybridizable, a hybrid Raviart–Thomas, or a hybrid Brezzi–Douglas–Marini) discretization of a Stokes problem. Our analysis is centered around the augmented Lagrangian approach and we prove uniform convergence in this setting. Beyond this, we establish relations

Higherorder adaptive methods for exit times of Itô diffusions IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231019
Håkon Hoel, Sankarasubramanian RagunathanWe construct a higherorder adaptive method for strong approximations of exit times of Itô stochastic differential equations (SDEs). The method employs a strong Itô–Taylor scheme for simulating SDE paths, and adaptively decreases the step size in the numerical integration as the solution approaches the boundary of the domain. These techniques complement each other nicely: adaptive timestepping improves

A local energybased discontinuous Galerkin method for fourthorder semilinear wave equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231016
Lu ZhangThis paper proposes an energybased discontinuous Galerkin scheme for fourthorder semilinear wave equations, which we rewrite as a system of secondorder spatial derivatives. Compared to the local discontinuous Galerkin methods, the proposed scheme uses fewer auxiliary variables and is more computationally efficient. We prove several properties of the scheme. For example, we show that the scheme is

Mixed Virtual Element approximation of linear acoustic wave equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231014
Franco Dassi, Alessio Fumagalli, Ilario Mazzieri, Giuseppe VaccaWe design a Mixed Virtual Element Method for the approximated solution to the firstorder form of the acoustic wave equation. In the absence of external loads, the semidiscrete method exactly conserves the system energy. To integrate in time the semidiscrete problem we consider a classical $\theta $method scheme. We carry out the stability and convergence analysis in the energy norm for the semidiscrete

Convergence of Lagrange finite element methods for Maxwell eigenvalue problem in 3D IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231014
Daniele Boffi, Sining Gong, Johnny Guzmán, Michael NeilanWe prove convergence of the Maxwell eigenvalue problem using quadratic or higher Lagrange finite elements on Worsey–Farin splits in three dimensions. To do this, we construct two Fortinlike operators to prove uniform convergence of the corresponding source problem. We present numerical experiments to illustrate the theoretical results.

A new step size selection strategy for the superiorization methodology using subgradient vectors and its application for solving convex constrained optimization problems IMA J. Numer. Anal. (IF 2.1) Pub Date : 20231010
Mokhtar Abbasi, Mahdi Ahmadinia, Ali AhmadiniaThis paper presents a novel approach for solving convex constrained minimization problems by introducing a special subclass of quasinonexpansive operators and combining them with the superiorization methodology that utilizes subgradient vectors. Superiorization methodology tries to reduce a target function while seeking a feasible point for the given constraints. We begin by introducing a new class

Milstein schemes and antithetic multilevel Monte Carlo sampling for delay McKean–Vlasov equations and interacting particle systems IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230906
Jianhai Bao, Christoph Reisinger, Panpan Ren, Wolfgang StockingerIn this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean–Vlasov stochastic differential equations, possibly with a drift term exhibiting superlinear growth in the state component. We prove strong convergence of order one and moment stability, making use of techniques from variational calculus on the space of probability measures with finite

Discrete Gagliardo–Nirenberg inequality and application to the finite volume approximation of a convection–diffusion equation with a Joule effect term IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230830
Caterina Calgaro, Clément Cancès, Emmanuel CreuséA discrete ordertwo Gagliardo–Nirenberg inequality is established for piecewise constant functions defined on a twodimensional structured mesh composed of rectangular cells. As in the continuous framework, this discrete Gagliardo–Nirenberg inequality allows to control in particular the $L^4$ norm of the discrete gradient of the numerical solution by the $L^2$ norm of its discrete Hessian times its

An arbitraryorder discrete rotrot complex on polygonal meshes with application to a quadrot problem IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230829
Daniele A Di PietroIn this work, following the discrete de Rham approach, we develop a discrete counterpart of a twodimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary approximation orders. We establish exactness on a contractible domain for both the versions of the complex with and without boundary conditions and, for the former, prove a complete

A nodally boundpreserving finite element method IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230826
Gabriel R Barrenechea, Emmanuil H Georgoulis, Tristan Pryer, Andreas VeeserThis work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into boundpreserving ones and seeks the numerical solution in the range of this projection. As the projection is not injective, a stabilisation based upon the complementary projection is added

Numerical approximation of singulardegenerate parabolic stochastic partial differential equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230825
Ľubomír Baňas, Benjamin Gess, Christian ViethWe study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) that include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully discrete numerical approximation of the considered SPDEs based on the very weak formulation. By exploiting the monotonicity properties of the proposed formulation

High order approximations of the Cox–Ingersoll–Ross process semigroup using random grids IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230825
Aurélien Alfonsi, Edoardo LombardoWe present new high order approximations schemes for the Cox–Ingersoll–Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021, A generic construction for high order approximation schemes of semigroups using random grids. Numer. Math., 148, 743–793) for the approximation of semigroups. The idea consists in using a suitable combination of discretization

A secondorder bulk–surface splitting for parabolic problems with dynamic boundary conditions IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230812
Robert Altmann, Christoph ZimmerThis paper introduces a novel approach for the construction of bulk–surface splitting schemes for semilinear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation of the system as a partial differential–algebraic equation and the inclusion of certain delay terms for the decoupling. To obtain a fully discrete scheme, the splitting

Optimized Schwarz methods for the timedependent Stokes–Darcy coupling IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230805
Marco Discacciati, Tommaso VanzanThis paper derives optimized coefficients for optimized Schwarz iterations for the timedependent Stokes–Darcy problem using an innovative strategy to solve a nonstandard minmax problem. The coefficients take into account both physical and discretization parameters that characterize the coupled problem, and they guarantee the robustness of the associated domain decomposition method. Numerical results

On symmetric positive definite preconditioners for multiple saddlepoint systems IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230805
John W Pearson, Andreas PotschkaWe consider symmetric positive definite preconditioners for multiple saddlepoint systems of block tridiagonal form, which can be applied within the Minres algorithm. We describe such a preconditioner for which the preconditioned matrix has only two distinct eigenvalues, $1$ and $1$, when the preconditioner is applied exactly. We discuss the relative merits of such an approach compared to a more widely

A posteriori error analysis of spacetime discontinuous Galerkin methods for the εstochastic Allen–Cahn equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230803
Dimitra C Antonopoulou, Bernard Egwu, Yubin YanIn this work, we apply an a posteriori error analysis for the spacetime, discontinuous in time, Galerkin scheme, which has been proposed in Antonopoulou (2020, Spacetime discontinuous Galerkin methods for the $\varepsilon $dependent stochastic Allen–Cahn equation with mild noise. IMA J. Num. Analysis, 40, 2076–2105) for the $\varepsilon $dependent stochastic Allen–Cahn equation with mild noise

Optimal numerical integration and approximation of functions on ℝd equipped with Gaussian measure IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230803
Dinh Dũng, Van Kien NguyenWe investigate the numerical approximation of integrals over $\mathbb{R}^{d}$ equipped with the standard Gaussian measure $\gamma $ for integrands belonging to the Gaussianweighted Sobolev spaces $W^{\alpha }_{p}(\mathbb{R}^{d}, \gamma )$ of mixed smoothness $\alpha \in \mathbb{N}$ for $1 < p < \infty $. We prove the asymptotic order of the convergence of optimal quadratures based on $n$ integration

The Gaussian wave packet transform via quadrature rules IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230729
Paul Bergold, Caroline LasserWe analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of squareintegrable functions is presented. Including a rigorous error analysis, the variants of the wave packet transform are then derived by a discretization of the Fourier integral via different quadrature

On the reduction in accuracy of finite difference schemes on manifolds without boundary IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230720
Brittany Froese Hamfeldt, Axel G R TurnquistWe investigate error bounds for numerical solutions of divergence structure linear elliptic partial differential equations (PDEs) on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of stability that guarantees the existence of a bounded solution. In many settings including the Dirichlet problem, it is easy to show

Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newtontype methods via range invariance IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230720
Barbara KaltenbacherA key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear illposed operator equations—such as coefficient identification in partial differential equations (PDEs) from boundary observations—can often be achieved by extending the searched for parameter in the sense of allowing it to depend on additional variables.

Adapting the centred simplex gradient to compensate for misaligned sample points IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230719
Yiwen Chen, Warren HareThe centred simplex gradient (CSG) is a popular gradient approximation technique in derivativefree optimization. Its computation requires a perfectly symmetric set of sample points and is known to provide an accuracy of $\mathcal {O}(\varDelta ^2)$, where $\varDelta $ is the radius of the sampling set. In this paper, we consider the situation where the set of sample points is not perfectly symmetric

Adaptive interior penalty hybridized discontinuous Galerkin methods for Darcy flow in fractured porous media IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230719
Haitao Leng, Huangxin ChenIn this paper, we design and analyze an interior penalty hybridized discontinuous Galerkin (IPHDG) method for the Darcy flow in the two and threedimensional fractured porous media. The discrete fracture model is used to model the fractures. The piecewise polynomials of degree $k$ are employed to approximate the pressure in the fractures and the pressure in the surrounding porous media. We prove

A unified approach to maximumnorm a posteriori error estimation for secondorder time discretizations of parabolic equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230705
Torsten Linβ, Martin Ossadnik, Goran RadojevA class of linear parabolic equations is considered. We derive a common framework for the a posteriori error analysis of certain secondorder time discretizations combined with finite element discretizations in space. In particular, we study the Crank–Nicolson method, the extrapolated Euler method, the backward differentiation formula of order 2, the Lobatto IIIC method and a twostage SDIRK method

Error analysis of timediscrete random batch method for interacting particle systems and associated meanfield limits IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230624
Xuda Ye, Zhennan ZhouThe random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially in terms of approximating the invariant distribution. The triangle inequality framework employed in this paper is a convenient approach to estimate the longtime

Nodal discrete duality numerical scheme for nonlinear diffusion problems on general meshes IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230620
Boris Andreianov, El Houssaine QuenjelDiscrete duality finite volume (DDFV) schemes are known for their ability to approximate nonlinear and linear anisotropic diffusion operators on general meshes, but they possess several drawbacks. The most important drawback of DDFV is the simultaneous use of the cell and the node unknowns. We propose a discretization approach that incorporates DDFV ideas and the associated analysis techniques, but

An augmented fully mixed formulation for the quasistatic Navier–Stokes–Biot model IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230620
Tongtong Li, Sergio Caucao, Ivan YotovWe introduce and analyze a partially augmented fully mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Navier–Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of fluid

Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230610
Sören Bartels, Balázs Kovács, Zhangxian WangAn error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unitlength constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.

Simultaneous diagonalization of nearly commuting Hermitian matrices: doonethendotheother IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230610
Brian D SuttonCommuting Hermitian matrices may be simultaneously diagonalized by a common unitary matrix. However, the numerical aspects are delicate. We revisit a previously rejected numerical approach in a new algorithm called ‘doonethendotheother’. One of two input matrices is diagonalized by a unitary similarity, and then the computed eigenvectors are applied to the other input matrix. Additional passes

Nonasymptotic estimates for TUSLA algorithm for nonconvex learning with applications to neural networks with ReLU activation function IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230610
DongYoung Lim, Ariel Neufeld, Sotirios Sabanis, Ying ZhangWe consider nonconvex stochastic optimization problems where the objective functions have superlinearly growing and discontinuous stochastic gradients. In such a setting, we provide a nonasymptotic analysis for the tamed unadjusted stochastic Langevin algorithm (TUSLA) introduced in Lovas et al. (2020). In particular, we establish nonasymptotic error bounds for the TUSLA algorithm in Wasserstein1

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230610
Dilara Abdel, Claire ChainaisHillairet, Patricio Farrell, Maxime HerdaIn this paper, we consider a driftdiffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g., due to Fermi–Dirac statistics). To incorporate volume exclusion effects, we rely on the Fermi–Dirac integral of order $1$ when modeling moving anionic vacancies within the perovskite layer, which is sandwiched

Scaling of radial basis functions IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230609
Elisabeth Larsson, Robert SchabackThis paper studies the influence of scaling on the behavior of radial basis function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The most important questions are: How does the error of a kernelbased interpolant vary with the scale of the kernel chosen? How does the standard error bound vary? And since fixed functions may be in spaces that allow scalings

Continuous interior penalty stabilization for divergencefree finite element methods IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230609
Gabriel R Barrenechea, Erik Burman, Ernesto Cáceres, Johnny GuzmánIn this paper, we propose, analyze and test numerically a pressurerobust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these

Multilevel quasiMonte Carlo for random elliptic eigenvalue problems I: regularity and error analysis IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230609
Alexander D Gilbert, Robert ScheichlStochastic partial differential equation (PDE) eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic crystal structures. In this paper we present a multilevel quasiMonte Carlo (MLQMC) method for approximating the expectation of the

Finite volumes for the Stefan–Maxwell crossdiffusion system IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230609
Clément Cancès, Virginie Ehrlacher, Laurent MonasseThe aim of this work is to propose a provably convergent finite volume scheme for the socalled Stefan–Maxwell model, which describes the evolution of the composition of a multicomponent mixture and reads as a crossdiffusion system. The scheme proposed here relies on a twopoint flux approximation, and preserves at the discrete level some fundamental theoretical properties of the continuous models

When can forward stable algorithms be composed stably? IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230529
Carlos Beltrán, Vanni Noferini, Nick VannieuwenhovenWe state some widely satisfied hypotheses, depending only on two functions $g$ and $h$, under which the composition of a forward stable algorithm for $g$ and a forward stable algorithm for $h$ is a forward stable algorithm for the composition $g \circ h$. We show that the failure of these conditions can potentially lead to unstable algorithms. Finally, we list a number of examples to illustrate the

A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230527
Juan Manuel Cárdenas, Manuel SolanoThis work analyses a highorder hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG solution can be computed. The introduction of the rotation as one of the unknowns allows us to use the gradient of the displacements to obtain an explicit representation

Convergence rate of inertial forward–backward algorithms based on the local error bound condition IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230526
Hongwei Liu, Ting Wang, Zexian LiuThe ‘inertial forward–backward algorithm’ (IFB) is a powerful algorithm for solving a class of convex nonsmooth minimization problems, IFB relies on an inertial parameter $\gamma _{k}$ whose tuning is crucial for achieving accelerated convergence speeds as compared to the classical forward–backward algorithm. Under the local error bound condition, it is known that IFB converges Rlinearly as soon