样式： 排序： IF:  GO 导出 标记为已读

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

A radiation box domain truncation scheme for the wave equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230525
B Schweizer, M Schäffner, Y TjandrawidjajaWe consider the wave equation in an unbounded domain and are interested in domain truncation methods. Our aim is to develop a numerical scheme that allows calculations for truncated waveguide geometries with periodic coefficient functions. The scheme is constructed with radiation boxes that are attached to the artificially introduced boundaries. A DirichlettoNeumann operator $N$ is calculated in

Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230524
Xiaobing Feng, Akash Ashirbad Panda, Andreas ProhlIn this paper, a higher order timediscretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ variational method for its error analysis and prove an improved convergence order of $\frac 32$ for the approximates of the solution. The core of the analysis is Hölder

Improved uniform error bounds on timesplitting methods for the longtime dynamics of the weakly nonlinear Dirac equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230524
Weizhu Bao, Yongyong Cai, Yue FengImproved uniform error bounds on timesplitting methods are rigorously proven for the longtime dynamics of the weakly nonlinear Dirac equation (NLDE), where the nonlinearity strength is characterized by a dimensionless parameter $\varepsilon \in (0, 1]$. We adopt a secondorder Strang splitting method to discretize the NLDE in time, and combine with the Fourier pseudospectral method in space for the

A fully mixed virtual element method for Darcy–Forchheimer miscible displacement of incompressible fluids appearing in porous media IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230522
Mehdi Dehghan, Zeinab GharibiThe incompressible miscible displacement of twodimensional Darcy–Forchheimer flow is discussed in this paper, and the mathematical model is formulated by two partial differential equations, a Darcy–Forchheimer flow equation for the pressure and a convection–diffusion equation for the concentration. The model is discretized using a fully mixed virtual element method (VEM), which employs mixed VEMs

Multilevel quasiMonte Carlo for random elliptic eigenvalue problems II: efficient algorithms and numerical results IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230519
Alexander D Gilbert, Robert ScheichlStochastic partial differential equation (PDE) eigenvalue problems (EVPs) often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper, we present an efficient multilevel quasiMonte Carlo (MLQMC) algorithm for computing the expectation of the smallest eigenvalue of an elliptic EVP with stochastic coefficients

Constrained and composite optimization via adaptive sampling methods IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230516
Yuchen Xie, Raghu Bollapragada, Richard Byrd, Jorge NocedalThe motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems, in which the objective function is stochastic and the constraints are deterministic. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min $f(x) + h(x)$, where $f$ is stochastic and $h$

Euler simulation of interacting particle systems and McKean–Vlasov SDEs with fully superlinear growth drifts in space and interaction IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230511
Xingyuan Chen, Gonçalo dos ReisThis work addresses the convergence of a splitstep Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean–Vlasov stochastic differential equations (MVSDEs) with full superlinear growth in the spatial and the interaction component in the drift, and nonconstant Lipschitz diffusion coefficient. Superlinearity is understood

Pressure robust SUPGstabilized finite elements for the unsteady Navier–Stokes equation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230509
L Beirão da Veiga, F Dassi, G VaccaIn the present contribution, we propose a novel conforming finite element scheme for the timedependent Navier–Stokes equation, which is proven to be both convection quasirobust and pressure robust. The method is built combining a ‘divergencefree’ velocity/pressure couple (such as the Scott–Vogelius element), a discontinuous Galerkin in time approximation and a suitable streamline upwind Petrov–Galerkincurl

Lax dynamics for Cartan decomposition with applications to Hamiltonian simulation IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230426
Moody T ChuSimulating the time evolution of a Hamiltonian system on a classical computer is hard—The computational power required to even describe a quantum system scales exponentially with the number of its constituents, let alone integrate its equations of motion. Hamiltonian simulation on a quantum machine is a possible solution to this challenge—Assuming that a quantum system composing of spin½ particles

A pressurerobust HHO method for the solution of the incompressible Navier–Stokes equations on general meshes IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230413
Daniel Castanon Quiroz, Daniele A Di PietroIn a recent work (Castanon Quiroz & Di Pietro (2020) A hybrid highorder method for the incompressible Navier–Stokes problem robust for large irrotational body forces. Comput. Math. Appl., 79, 2655–2677), we have introduced a pressurerobust hybrid highorder method for the numerical solution of the incompressible Navier–Stokes equations on matching simplicial meshes. Pressurerobust methods are characterized

Regularity analysis for SEEs with multiplicative fBms and strong convergence for a fully discrete scheme IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230412
XiaoLi Ding, Dehua WangOne of the open problems in the study of stochastic differential equations is regularity analysis and approximations to stochastic partial differential equations driven by multiplicative fractional Brownian motions (fBms), especially for the case $H\in (0,\frac {1}{2})$. In this paper, we address this problem by considering a class of stochastic evolution equations (SEEs) driven by multiplicative fBms

Stability and convergence analysis of highorder numerical schemes with DtNtype absorbing boundary conditions for nonlocal wave equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230404
Jihong Wang, Jerry Zhijian Yang, Jiwei ZhangThe stability and convergence analysis of highorder numerical approximations for the one and twodimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadraturebased finite difference schemes to discretize the spatially nonlocal operator, and apply the explicit difference scheme to approximate the temporal derivative to achieve a fully discrete infinity

Multiresolution analysis for stochastic hyperbolic conservation laws IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230321
M Herty, A Kolb, S MüllerA multiresolution analysis (MRA) for solving stochastic conservation laws is proposed. Using a novel adaptation strategy and a higherdimensional deterministic problem, a discontinuous Galerkin (DG) solver is derived. An MRA of the DG spaces for the proposed adaptation strategy is presented. Numerical results show that in the case of general stochastic distributions the performance of the DG solver

A hybrid highorder scheme for the stationary, incompressible magnetohydrodynamics equations IMA J. Numer. Anal. (IF 2.1) Pub Date : 20230317
Jérôme Droniou, Liam YemmWe propose and analyse a hybrid highorder scheme for the stationary incompressible magnetohydrodynamics equations. The scheme has an arbitrary order of accuracy and is applicable on generic polyhedral meshes. For sources that are small enough, we prove error estimates in energy norm for the velocity and magnetic field, and $L^2$norm for the pressure; these estimates are fully robust with respect