Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations
type: Item
instance of: scholarly article
title: Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations
author: Jiyuan Zhang
author: Yifan Qin
author: Qifeng Zhang
published in: Applied Numerical Mathematics
publication date: 2022-12-09T00:00:00Z
review text: The authors consider two types of two-dimensional nonlinear Sobolev equations and their numerical solutions obtained using two classes of higher-order numerical schemes on the time discretizations, and compact difference operator in spatial dimension. The main contribution of this paper is the proof the convergence in maximum norm for the compact difference scheme from [\textit{X. Chen} et al., Numer. Methods Partial Differ. Equations 34, No. 3, 1093--1112 (2018; Zbl 1407.65098)], as well as a new and more efficient three-level linearized compact difference scheme for solving the equations. The essential improvement for the three-level linearized compact difference scheme is that the coefficient matrix is fixed which costs much less CPU time then in the case of two-level scheme. The numerical tests which confirm the theoretical results and demonstrate the efficiency of both difference schemes are given.
reviewed by: Ljiljana Teofanov
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7630333
zbMATH Keywords: nonlinear Sobolev equation
zbMATH Keywords: compact difference scheme
zbMATH Keywords: energy method
zbMATH Keywords: maximum error estimate
MaRDI profile type: Publication
full work available at URL: j.apnum.2022.10.005
OpenAlex ID: W4307056316
cites work: Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation
cites work: Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation
cites work: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
cites work: A semilinear Sobolev evolution equation in a Banach space
cites work: Two-grid finite element methods combined with Crank-Nicolson scheme for nonlinear Sobolev equations
cites work: A Newton linearized compact finite difference scheme for one class of Sobolev equations
cites work: Application of spectral element method for solving Sobolev equations with error estimation
cites work: A new fourth‐order numerical algorithm for a class of three‐dimensional nonlinear evolution equations
cites work: A coupled non-linear hyperbolic-Sobolev system
cites work: Time-Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations
cites work: Numerical Solution of Sobolev Partial Differential Equations
cites work: Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation
cites work: Characteristic finite element methods for nonlinear Sobolev equations
cites work: A note on numerical solution of classical Darboux problem
cites work: Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations
cites work: Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin-Bona-Mahony-Burgers and Sobolev equations
cites work: Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher-Kolmogorov model
cites work: An expanded mixed finite element method for two-dimensional Sobolev equations
cites work: Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
cites work: Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
cites work: Galerkin methods for nonlinear Sobolev equations
cites work: A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation
cites work: A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations
cites work: Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension
cites work: L2-ERROR ANALYSIS OF FULLY DISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR NONLINEAR SOBOLEV EQUATIONS
cites work: Convergence of Galerkin approximations for the Kuramoto‐Tsuzuki equation
cites work: Q3572299
cites work: Superconvergence analysis of an \(H^1\)-Galerkin mixed finite element method for Sobolev equations
cites work: High accuracy analysis of a new nonconforming mixed finite element scheme for Sobolev equations
cites work: Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation
cites work: Unconditional superconvergence analysis of an H1‐galerkin mixed finite element method for nonlinear Sobolev equations
cites work: Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach Space
cites work: Sobolev equations for nonlinear dispersive systems†
cites work: The finite difference streamline diffusion methods for Sobolev equations with convection-dominated term
cites work: A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations
cites work: Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations
cites work: A linearized compact difference scheme for a class of nonlinear delay partial differential equations
cites work: A cooling process according to two-temperature theory of heat conduction
cites work: A posteriori error estimates with the finite element method of lines for a Sobolev equation
cites work: Some soliton-type analytical solutions and numerical simulation of nonlinear Schrödinger equation
cites work: Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations
cites work: Linearized compact difference methods combined with Richardson extrapolation for nonlinear delay Sobolev equations
cites work: A new space-time continuous Galerkin method with mesh modification for Sobolev equations
DOI: 10.1016/J.APNUM.2022.10.005
description: scientific article; zbMATH DE number 7630333