Two-grid finite volume element methods for semilinear parabolic problems
type: Item
instance of: scholarly article
title: Two-grid finite volume element methods for semilinear parabolic problems
zbMATH Open document ID: 1193.65161
author: Chuanjun Chen
author: Wei Liu
published in: Applied Numerical Mathematics
publication date: 2010-05-06T00:00:00Z
review text: The present paper presents a finite volume element method (FVEM) based on two finite element spaces defined on a coarse and a fine grid, applied to a parabolic semilinear problem. An appealing feature is that nonsymmetric and nonlinear problems on a fine space could be regarded as solving a symmetric linear problem on the fine space, plus a nonsymmetric nonlinear problem on the coarse space. The wellposedness of the FVEM is assessed using the Carathéodory theorem, and optimal convergence rates are derived for the one-grid and the two-grid method. Finally, a numerical example illustrates the behavior of the error predicted by the provided theoretical findings.
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5704975
zbMATH Keywords: vertex-centered finite volume
zbMATH Keywords: finite volume element method
zbMATH Keywords: error estimates
zbMATH Keywords: parabolic semilinear problem
zbMATH Keywords: convergence
zbMATH Keywords: two-grid method
zbMATH Keywords: numerical example
reviewed by: Ricardo Ruiz-Baier
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.08.004
OpenAlex ID: W2143874584
cites work: Some Error Estimates for the Box Method
cites work: Two-grid finite volume element method for linear and nonlinear elliptic problems
cites work: On the finite volume element method
cites work: On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids
cites work: Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
cites work: A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations
cites work: Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
cites work: Lp error estimates and superconvergence for covolume or finite volume element methods
cites work: Q4326672
cites work: A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations
cites work: Finite volume element approximations of nonlocal reactive flows in porous media
cites work: On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
cites work: On first and second order box schemes
cites work: $hp$-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems
cites work: Two-level Picard and modified Picard methods for the Navier-Stokes equations
cites work: Q4936091
cites work: Symmetric finite volume discretizations for parabolic problems.
cites work: Q4381925
cites work: Symmetric modified finite volume element methods for selfadjoint elliptic and parabolic problems
cites work: On Galerkin Methods in Semilinear Parabolic Problems
cites work: Two-grid finite element formulations of the incompressible Navier-Stokes equations
cites work: Q4702116
cites work: A Novel Two-Grid Method for Semilinear Elliptic Equations
cites work: Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
DOI: 10.1016/J.APNUM.2009.08.004
description: scientific article; zbMATH DE number 5704975