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Highresolution signal recovery via generalized sampling and functional principal component analysis Adv. Comput. Math. (IF 1.91) Pub Date : 20211123
Gataric, MilanaIn this paper, we introduce a computational framework for recovering a highresolution approximation of an unknown function from its lowresolution indirect measurements as well as highresolution training observations by merging the frameworks of generalized sampling and functional principal component analysis. In particular, we increase the signal resolution via a datadriven approach, which models

A divergencefree weak virtual element method for the NavierStokes equation on polygonal meshes Adv. Comput. Math. (IF 1.91) Pub Date : 20211115
Wang, Gang, Wang, Feng, He, YinnianIn this paper, we present a divergencefree weak virtual element method for the NavierStokes equation on polygonal meshes. The velocity and the pressure are discretized by the H(div) virtual element and discontinuous piecewise polynomials, respectively. An additional polynomial space that lives on the element edges is introduced to approximate the tangential trace of the velocity. The velocity at

A family of C1 quadrilateral finite elements Adv. Comput. Math. (IF 1.91) Pub Date : 20211103
Kapl, Mario, Sangalli, Giancarlo, Takacs, ThomasWe present a novel family of C1 quadrilateral finite elements, which define global C1 spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements extend the construction by Brenner and Sung (J. Sci. Comput. 22(13), 83118, 2005), which is based on polynomial elements of tensorproduct degree p ≥ 6, to all degrees p ≥ 3. The proposed C1 quadrilateral is based upon the

A fast and oblivious matrix compression algorithm for Volterra integral operators Adv. Comput. Math. (IF 1.91) Pub Date : 20211026
Dölz, J., Egger, H., Shashkov, V.The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretization, the basic problem can be represented as a matrixvector product with a lower diagonal but densely populated matrix. For typical applications, like fractional diffusion or largescale dynamical systems with delay, the memory

Essentially optimal finite elements for multiscale elliptic eigenvalue problems Adv. Comput. Math. (IF 1.91) Pub Date : 20211022
Muoi, Pham Quy, Tan, Wee Chin, Hoang, Viet HaWe consider a multiscale elliptic eigenvalue problem that depends on n separable microscopic scales. Using multiscale homogenization, we derive the multiscale homogenized eigenvalue problem whose solution contains all the possible eigenvalues and eigenfunctions of the homogenized eigenvalue problem. We develop the sparse tensor product finite element (FE) method for solving this multiscale homogenized

Correction to: Exponential meansquare stability properties of stochastic linear multistep methods Adv. Comput. Math. (IF 1.91) Pub Date : 20211018
Buckwar, Evelyn, D’Ambrosio, RaffaeleA Correction to this paper has been published: https://doi.org/10.1007/s10444021099017

Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation Adv. Comput. Math. (IF 1.91) Pub Date : 20211018
Liu, Wenjie, Wang, LiLian, Wu, BoyingWe present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and “interpolates” the usual Taylor formulas with two consecutive integer orders. This enables us to obtain an analogous formula for the Legendre expansion coefficient of this type of singular functions, and further derive the optimal (weighted) \(L^{\infty }\)estimates

Comparison of integral equations for the Maxwell transmission problem with general permittivities Adv. Comput. Math. (IF 1.91) Pub Date : 20211015
Helsing, Johan, Karlsson, Anders, Rosén, AndreasTwo recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for nonmagnetic materials. The winning integral equation turns out to be entirely free from false eigenwavenumbers for any passive materials, also for purely negative permittivity ratios and in the static limit, as well as free from false essential

An a posteriori error estimate for a dual mixed method applied to Stokes system with nonnull source terms Adv. Comput. Math. (IF 1.91) Pub Date : 20211015
Barrios, Tomás P., Behrens, Edwin M., Bustinza, RommelIn this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of completeness, we begin recalling the corresponding wellposedness at continuous and discrete levels. After that, and with the help of a kind of a quasiHelmholtz decomposition of functions in H(div), we develop a residual type a posteriori error analysis, deducing

Mixed precision path tracking for polynomial homotopy continuation Adv. Comput. Math. (IF 1.91) Pub Date : 20210929
Timme, SaschaThis article develops a new predictorcorrector algorithm for numerical path tracking in the context of polynomial homotopy continuation. In the corrector step, it uses a newly developed Newton corrector algorithm which rejects an initial guess if it is not an approximate zero. The algorithm also uses an adaptive step size control that builds on a local understanding of the region of convergence of

A rational RBF interpolation with conditionally positive definite kernels Adv. Comput. Math. (IF 1.91) Pub Date : 20210927
Farazandeh, Elham, Mirzaei, DavoudIn this paper, we present a rational RBF interpolation method to approximate multivariate functions with poles or other singularities on or near the domain of approximation. The method is based on scattered point layouts and is flexible with respect to the geometry of the problem’s domain. Despite the existing rational RBFbased techniques, the new method allows the use of conditionally positive definite

Accurate singular values of a class of parameterized negative matrices Adv. Comput. Math. (IF 1.91) Pub Date : 20210910
Huang, Rong, Xue, JungongTypically, parametrization captures the essence of a class of matrices, and its potential advantage is to make accurate computations possible. But, in general, parametrization suitable for accurate computations is not always easy to find. In this paper, we introduce a parametrization of a class of negative matrices to accurately solve the singular value problem. It is observed that, given a set of

Error analysis of the SAV Fourierspectral method for the CahnHilliardHeleShaw system Adv. Comput. Math. (IF 1.91) Pub Date : 20210910
Zheng, Nan, Li, XiaoliIn this paper, we construct several efficient scalar auxiliary variable (SAV) schemes based on the Fourierspectral method in space for the CahnHilliardHeleShaw system. The temporal discretizations are built upon the firstorder Euler and secondorder BDF method, respectively. We derive the unconditional energy stability for both schemes and also establish the rigorous error estimates for the firstorder

Carleman estimates and controllability results for fully discrete approximations of 1D parabolic equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210910
Casanova, Pedro González, HernándezSantamaría, VíctorIn this paper, we prove a Carleman estimate for fully discrete approximations of onedimensional parabolic operators in which the discrete parameters h and △t are connected to the large Carleman parameter. We use this estimate to obtain relaxed observability inequalities which yield, by duality, controllability results for fully discrete linear and semilinear parabolic equations.

An alternative approach for order conditions of RungeKuttaNyström methods Adv. Comput. Math. (IF 1.91) Pub Date : 20210907
Sun, Xue, Liu, Zhongli, Tian, HongjiongWe present an alternative approach proposed by Albrecht to derive general order conditions for RungeKuttaNyström methods and relate it to the classical RKNtheory. The RKNmethods are treated as composite linear methods to yield the general order conditions as orthogonal relations. We then exploit the orthogonal structure of the order conditions and obtain a simple recursion to generate the order

Kernel aggregated fast multipole method Adv. Comput. Math. (IF 1.91) Pub Date : 20210906
Yan, Wen, Blackwell, RobertMany different simulation methods for Stokes flow problems involve a common computationally intense task—the summation of a kernel function over O(N2) pairs of points. One popular technique is the kernel independent fast multipole method (KIFMM), which constructs a spatial adaptive octree for all points and places a small number of equivalent multipole and local equivalent points around each octree

Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification Adv. Comput. Math. (IF 1.91) Pub Date : 20210903
Graham, I. G., Pembery, O. R., Spence, E. A.This paper analyses the following question: let Aj, j = 1,2, be the Galerkin matrices corresponding to finiteelement discretisations of the exterior Dirichlet problem for the heterogeneous Helmholtz equations ∇⋅ (Aj∇uj) + k2njuj = −f. How small must \(\A_{1} A_{2}\_{L^{q}}\) and \(\{n_{1}}  {n_{2}}\_{L^{q}}\) be (in terms of kdependence) for GMRES applied to either \((\mathbf {A}_1)^{1}\mathbf

Robust preconditioning techniques for multiharmonic finite element method with application to timeperiodic parabolic optimal control problems Adv. Comput. Math. (IF 1.91) Pub Date : 20210903
Liang, ZhaoZheng, Zhang, GuoFengWe are concerned with efficient solutions of the timeperiodic parabolic optimal control problems. By using the multiharmonic FEM, the linear algebraic equations characterizing the firstorder optimality conditions can be decoupled into a series of parallel solvable block 4 × 4 linear systems with respect to the cosine and sine Fourier coefficients of the state and scaled control variables for different

An O(N) algorithm for computing expectation of Ndimensional truncated multivariate normal distribution I: fundamentals Adv. Comput. Math. (IF 1.91) Pub Date : 20210901
Huang, Jingfang, Cao, Jian, Fang, Fuhui, Genton, Marc G., Keyes, David E., Turkiyyah, GeorgeIn this paper, we present the fundamentals of a hierarchical algorithm for computing the Ndimensional integral \(\phi (\mathbf {a}, \mathbf {b}; A) = {\int \limits }_{\mathbf {a}}^{\mathbf {b}} H(\mathbf {x}) f(\mathbf {x}  A) \text {d} \mathbf {x}\) representing the expectation of a function H(X) where f(xA) is the truncated multivariate normal (TMVN) distribution with zero mean, x is the vector

Computing lowrank rightmost eigenpairs of a class of matrixvalued linear operators Adv. Comput. Math. (IF 1.91) Pub Date : 20210901
Guglielmi, Nicola, Kressner, Daniel, Scalone, CarmelaIn this article, a new method is proposed to approximate the rightmost eigenpair of certain matrixvalued linear operators, in a lowrank setting. First, we introduce a suitable ordinary differential equation, whose solution allows us to approximate the rightmost eigenpair of the linear operator. After analyzing the behaviour of its solution on the whole space, we project the ODE on a lowrank manifold

A fast ADI orthogonal spline collocation method with graded meshes for the twodimensional fractional integrodifferential equation Adv. Comput. Math. (IF 1.91) Pub Date : 20210831
Qiao, Leijie, Xu, DaWe propose and analyze a timestepping CrankNicolson(CN) alternating direction implicit(ADI) scheme combined with an arbitraryorder orthogonal spline collocation (OSC) methods in space for the numerical solution of the fractional integrodifferential equation with a weakly singular kernel. We prove the stability of the numerical scheme and derive error estimates. The analysis presented allows variable

An H1 convergence of the spectral method for the timefractional nonlinear diffusion equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210825
Zhang, Hui, Jiang, Xiaoyun, Zeng, FanhaiThe generalized discrete Gronwall inequality is applied to analyze the optimal H1 error estimate of the timestepping spectral method for the timefractional diffusion equations, where the timefractional derivative is discretized by the secondorder fractional backward difference formula or the secondorder generalized NewtonGregory formula. The methodology is extended to analyze the fractional Crank–Nicolson

Convergence rates for boundedly regular systems Adv. Comput. Math. (IF 1.91) Pub Date : 20210824
Csetnek, Ernö Robert, Eberhard, Andrew, Tam, Matthew K.In this work, we consider a continuous dynamical system associated with the fixed point set of a nonexpansive operator which was originally studied by Boţ and Csetnek (J. Dyn. Diff. Equat. 29(1), pp. 155–168, 2017). Our main results establish convergence rates for the system’s trajectories when the nonexpansive operator satisfies an additional regularity property. This setting is the natural continuoustime

Nonsymmetric isogeometric FEMBEM couplings Adv. Comput. Math. (IF 1.91) Pub Date : 20210819
Elasmi, Mehdi, Erath, Christoph, Kurz, StefanWe present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either twodimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly nonlinear materials. The Boundary Element Method is applied in unbounded or thin domains

Rapid evaluation of the spectral signal detection threshold and Stieltjes transform Adv. Comput. Math. (IF 1.91) Pub Date : 20210813
Leeb, WilliamAccurate detection of signal components is a frequentlyencountered challenge in statistical applications with a low signaltonoise ratio. This problem is particularly challenging in settings with heteroscedastic noise. In certain signalplusnoise models of data, such as the classical spiked covariance model and its variants, there are closed formulas for the spectral signal detection threshold (the

Efficient spatial second/fourthorder finite difference ADI methods for multidimensional variableorder timefractional diffusion equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210806
Fu, Hongfei, Zhu, Chen, Liang, Xueting, Zhang, BingyinVariableorder timefractional diffusion equations (VOtFDEs), which can be used to model solute transport in heterogeneous porous media are considered. Concerning the wellposedness and regularity theory (cf., Zheng & Wang, Anal. Appl., 2020), two finite difference ADI and compact ADI schemes are respectively proposed for the twodimensional VOtFDE. We show that the two schemes are unconditionally

Estimating the error in matrix function approximations Adv. Comput. Math. (IF 1.91) Pub Date : 20210803
Eshghi, Nasim, Reichel, LotharThe need to compute matrix functions of the form f(A)v, where \(A\in {\mathbb {R}}^{N\times N}\) is a large symmetric matrix, f is a function such that f(A) is well defined, and v≠ 0 is a vector, arises in many applications. This paper is concerned with the situation when A is so large that the evaluation of f(A) is prohibitively expensive. Then, an approximation of f(A)v often is computed by applying

Cayleytransformbased gradient and conjugate gradient algorithms on Grassmann manifolds Adv. Comput. Math. (IF 1.91) Pub Date : 20210730
Zhu, Xiaojing, Sato, HiroyukiIn this paper, we study Cayleytransformbased gradient and conjugate gradient algorithms for optimization on Grassmann manifolds. We revisit the Cayley transform on Grassmann manifolds as a retraction in the framework of quotient manifolds constructed by Lie group actions and obtain an efficient formula for this retraction in lowrank cases. We also prove that this retraction is the restriction of

Exponential meansquare stability properties of stochastic linear multistep methods Adv. Comput. Math. (IF 1.91) Pub Date : 20210726
Evelyn Buckwar, Raffaele D’AmbrosioThe aim of this paper is the analysis of exponential meansquare stability properties of nonlinear stochastic linear multistep methods. In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential meansquare contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand

When is there a representer theorem? Adv. Comput. Math. (IF 1.91) Pub Date : 20210720
Kevin SchlegelWe consider a general regularised interpolation problem for learning a parameter vector from data. The wellknown representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is at the core of kernel methods in machine learning as it makes the problem computationally tractable. Most literature deals only with sufficient

Continuous window functions for NFFT Adv. Comput. Math. (IF 1.91) Pub Date : 20210630
Daniel Potts, Manfred TascheIn this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here, we consider the continuous Kaiser–Bessel, continuous exptype, sinhtype, and continuous coshtype window functions with the same support and same shape parameter. We present novel explicit

Optimal superconvergence analysis for the CrouzeixRaviart and the Morley elements Adv. Comput. Math. (IF 1.91) Pub Date : 20210629
Jun Hu, Limin Ma, Rui MaIn this paper, an improved superconvergence analysis is presented for both the CrouzeixRaviart element and the Morley element. The main idea of the analysis is to employ a discrete Helmholtz decomposition of the difference between the canonical interpolation and the finite element solution for the firstorder mixed Raviart–Thomas element and the mixed Hellan–Herrmann–Johnson element, respectively

Clothoid fitting and geometric Hermite subdivision Adv. Comput. Math. (IF 1.91) Pub Date : 20210626
Ulrich Reif, Andreas WeinmannWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive

Learning via variably scaled kernels Adv. Comput. Math. (IF 1.91) Pub Date : 20210626
C. Campi, F. Marchetti, E. PerracchioneWe investigate the use of the socalled variably scaled kernels (VSKs) for learning tasks, with a particular focus on support vector machine (SVM) classifiers and kernel regression networks (KRNs). Concerning the kernels used to train the models, under appropriate assumptions, the VSKs turn out to be more expressive and more stable than the standard ones. Numerical experiments and applications to breast

Translation partitions of unity, symmetry properties, and Gabor frames Adv. Comput. Math. (IF 1.91) Pub Date : 20210625
Ole Christensen, Say Song Goh, Hong Oh Kim, Rae Young KimWe consider the general question of constructing a partition of unity formed by translates of a compactly supported function g : ℝd → ℂ. In particular, we prove that such functions have a special structure that simplifies the construction of partitions of unity with specific properties. We also prove that it is possible to modify the function g in such a way that it becomes symmetric with respect to

Adaptive sampling and modal expansions in patternforming systems Adv. Comput. Math. (IF 1.91) Pub Date : 20210616
M.L. Rapún, F. Terragni, J. M. VegaA new sampling technique for the application of proper orthogonal decomposition to a set of snapshots has been recently developed by the authors to facilitate a variety of data processing tasks (J. Comput. Phys. 335, 2017). According to it, robust modal expansions result from performing the decomposition on a limited number of relevant snapshots and a limited number of discretization mesh points, which

Cssmooth isogeometric spline spaces over planar bilinear multipatch parameterizations Adv. Comput. Math. (IF 1.91) Pub Date : 20210530
Mario Kapl, Vito VitrihThe design of globally Cssmooth (s ≥ 1) isogeometric spline spaces over multipatch geometries with possibly extraordinary vertices, i.e. vertices with valencies different from four, is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods Kapl et al. Comput. Aided Geom. Des. 52–53:75–89, 2017, Kapl et al. Comput. Aided Geom

A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integrodifferential constitutive law Adv. Comput. Math. (IF 1.91) Pub Date : 20210527
Yongseok Jang, Simon ShawWe consider a fractional order viscoelasticity problem modelled by a powerlaw type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the

Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators Adv. Comput. Math. (IF 1.91) Pub Date : 20210521
Bowei Wu, PerGunnar MartinssonA highorder accurate quadrature rule for the discretization of boundary integral equations (BIEs) on closed smooth contours in the plane is introduced. This quadrature can be viewed as a hybrid of the spectral quadrature of Kress (Math. Comput. Model. 15(35), 229–243 1991) and the locally corrected trapezoidal quadrature of Kapur and Rokhlin (SIAM J. Numer. Anal. 34(4), 1331–1356, 1997). The new

Multivariate quadrature of a singular integrand Adv. Comput. Math. (IF 1.91) Pub Date : 20210514
Kendall Atkinson, David Chien, Olaf HansenConsider an integral with a point singularity in its integrand, such as ρ−α or \(\log \rho \). We introduceand discuss two methods for approximating such integrals, in both two and three dimensions. The methods are first introduced using the unit disk as the quadrature region, and then, they are extended to other regions and to three dimensions. The error behavior of the numerical integration for singular

Structurepreserving interpolation of bilinear control systems Adv. Comput. Math. (IF 1.91) Pub Date : 20210511
Peter Benner, Serkan Gugercin, Steffen W. R. WernerIn this paper, we extendthe structurepreserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for singleinput singleoutput

A fast sparse spectral method for nonlinear integrodifferential Volterra equations with general kernels Adv. Comput. Math. (IF 1.91) Pub Date : 20210507
Timon S. GutlebWe present a sparse spectral method for nonlinear integrodifferential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolutiontype kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical

A characteristic finite element method for the timefractional mobile/immobile advection diffusion model Adv. Comput. Math. (IF 1.91) Pub Date : 20210506
Huan Liu, Xiangcheng Zheng, Chuanjun Chen, Hong WangIn this paper, we study the solute transport in heterogeneous media described by the timefractional mobile/immobile advection diffusion model, where the integer and the fractional time derivatives are employed to characterize the movement of the particles in the mobile and immobile zone, respectively. We propose a fully discrete characteristic finite element scheme for the model, in which the modified

Reconstruction of lowrank aggregation kernels in univariate population balance equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210502
Robin Ahrens, Sabine Le BorneThe dynamics of particle processes can be described by population balance equations which are governed by phenomena including growth, nucleation, breakage and aggregation. Estimating the kinetics of the aggregation phenomena from measured density data constitutes an illconditioned inverse problem. In this work, we focus on the aggregation problem and present an approach to estimate the aggregation

A hybrid collocationperturbation approach for PDEs with random domains Adv. Comput. Math. (IF 1.91) Pub Date : 20210502
Julio E. CastrillónCandás, Fabio Nobile, Raúl F. TemponeConsider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into large and small variations contributions. The large variations are approximated by applying a sparse grid stochastic collocation method. The small

An hp version Legendre spectral collocation method for multiorder fractional differential equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210422
Yuling Guo, Zhongqing WangIn this paper, we consider the multiorder fractional differential equation and recast it into an integral equation. Based on the integral equation, we develop an hpversion Legendre spectral collocation method and the integral terms with the weakly singular kernels are calculated precisely according to the properties of Legendre and Jacobi polynomials. The hpversion error bounds under the L2norm

A spacetime certified reduced basis method for quasilinear parabolic partial differential equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210422
Michael Hinze, Denis KorolevIn this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential operator. We provide a residualbased a posteriori error estimate for a spacetime formulation and the corresponding efficiently computable bound for the certification of the method. We introduce a PetrovGalerkin finite element discretization of the continuous

Secondorder accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials Adv. Comput. Math. (IF 1.91) Pub Date : 20210422
Yubing Sui, Jingzhou Jiang, Guigen Jin, Xiaofeng YangWe consider in this paper numerical approximations of the immiscible binary mixture of nematic liquid crystals (LCs) and viscous fluids. We develop a secondorder time marching scheme by adopting the recently developed stabilizedSAV (scalar auxiliary variable) approach where several critical stabilization terms are added to enhance the stability; thus, large time steps are allowed in computations

Pointwise error estimate in difference setting for the twodimensional nonlinear fractional complex GinzburgLandau equation Adv. Comput. Math. (IF 1.91) Pub Date : 20210420
Qifeng Zhang, Jan S. Hesthaven, Zhizhong Sun, Yunzhu RenIn this paper, we propose a threelevel linearized implicit difference scheme for the twodimensional spatial fractional nonlinear complex GinzburgLandau equation. We prove that the difference scheme is stable and convergent under mild conditions. The optimal convergence order \(\mathcal {O}(\tau ^{2}+{h_{x}^{2}}+{h_{y}^{2}})\) is obtained in the pointwise sense by developing a new twodimensional

Convergence analysis of the scaled boundary finite element method for the Laplace equation Adv. Comput. Math. (IF 1.91) Pub Date : 20210419
Fleurianne Bertrand, Daniele Boffi, Gonzalo G. de DiegoThe scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (PDEs) without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semidiscrete functions and constructing an interpolation

Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval Adv. Comput. Math. (IF 1.91) Pub Date : 20210419
Nguyen Hieu Thao, Oleg Soloviev, Michel VerhaegenWe present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results

Variational Bayesian inversion for the reaction coefficient in spacetime nonlocal diffusion equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210417
Xiaoyan Song, GuangHui Zheng, Lijian JiangIn the paper, a variational Bayesian method is used to identify the reaction coefficient for spacetime nonlocal diffusion equations using nonlocal averaged flux data. To show the posterior measure to be welldefined, we rigorously prove that the forward operator is continuous with respect to the unknown reaction field. Then, gradientbased prior information is proposed to explore oscillation features

Residualtype a posteriori error analysis of HDG methods for Neumann boundary control problems Adv. Comput. Math. (IF 1.91) Pub Date : 20210417
Haitao Leng, Yanping ChenWe study a posteriori error analysis of linearquadratic boundary control problems under bilateral box constraints on the control which acts through a Neumanntype boundary condition. We adopt the hybridizable discontinuous Galerkin method as the discretization technique, and the flux variables, the scalar variables, and the boundary trace variables are all approximated by polynomials of degree k.

A quadratic finite volume method for nonlinear elliptic problems Adv. Comput. Math. (IF 1.91) Pub Date : 20210417
Yuanyuan Zhang, Chuanjun Chen, Chunjia BiIn this paper, we consider a quadratic finite volume method (FVM) for solving secondorder nonlinear elliptic problems. Under reasonable assumptions, we shall establish the existence and uniqueness of the quadratic FVM approximation and develop the error analysis of the approximation solution. To be specific, without any additional requirements on the underlying triangular meshes, we derive the optimal

Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils Adv. Comput. Math. (IF 1.91) Pub Date : 20210410
Jiaofen Li, Wen Li, Xuefeng Duan, Mingqing XiaoThe l parameterized generalized eigenvalue problems for the nonsquare matrix pencils, proposed by Chu et al.in 2006, can be formulated as an optimization problem on a corresponding complex product Stiefel manifold. In this paper, an effective and efficient algorithm based on the Riemannian Newton’s method is established to solve the underlying problem. Under our proposed framework, to solve the corresponding

A stabilizerfree pressurerobust finite element method for the Stokes equations Adv. Comput. Math. (IF 1.91) Pub Date : 20210408
Xiu Ye, Shangyou ZhangIn this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocitypressure formulation using H(div) finite elements to approximate velocity. Like other finite element methods with velocity discretized by H(div) conforming elements, our method has the advantages of an exact divergencefree velocity field and pressurerobustness. However, most of H(div)

Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems Adv. Comput. Math. (IF 1.91) Pub Date : 20210407
Fei Xu, Meiling Yue, Bin ZhengLargescale nonsymmetric eigenvalue problems are common in various fields of science and engineering computing. However, their efficient handling is challenging, and research on their solution algorithms is limited. In this study, a new multilevel correction adaptive finite element method is designed for solving nonsymmetric eigenvalue problems based on the adaptive refinement technique and multilevel

Randomized linear algebra for model reduction—part II: minimal residual methods and dictionarybased approximation Adv. Comput. Math. (IF 1.91) Pub Date : 20210326
Oleg Balabanov, Anthony NouyA methodology for using random sketching in the context of model order reduction for highdimensional parameterdependent systems of equations was introduced in Balabanov and Nouy (Part I; Advances in Computational Mathematics 45:2969–3019, 2019). Following this framework, we here construct a reduced model from a small, efficiently computable random object called a sketch of a reduced model, using

p  and hp  virtual elements for the Stokes problem Adv. Comput. Math. (IF 1.91) Pub Date : 20210323
A. Chernov, C. Marcati, L. MascottoWe analyse the p and hpversions of the virtual element method (VEM) for the Stokes problem on polygonal domains. The key tool in the analysis is the existence of a bijection between Poissonlike and Stokeslike VE spaces for the velocities. This allows us to reinterpret the standard VEM for Stokes as a VEM, where the test and trial discrete velocities are sought in Poissonlike VE spaces. The upside

Joint spectral radius and ternary hermite subdivision Adv. Comput. Math. (IF 1.91) Pub Date : 20210323
M. Charina, C. Conti, T. Mejstrik, J.L. MerrienIn this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and \({\mathscr{H}}\mathcal {C}^{2}\)smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a twoparameter family whose \({\mathscr{H}}\mathcal