Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
type: Item
instance of: scholarly article
title: Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
zbMATH Open document ID: 0891.65099
author: A. Ditkowski
author: Saul S. Abarbanel
published in: Journal of Computational Physics
publication date: 1998-07-01T00:00:00Z
review text: A finite difference scheme for a multidimensional diffusion equation with constant coefficients in a domain with complex shape is described. The scheme in based on a rectangular grid, has fourth-order spatial approximation, and is asymptotically stable in time. The error estimate is based on the property that the symmetric part of the matrix corresponding to the spatial discretization is negative definite. The Dirichlet boundary conditions are imposed in a penalty-like manner. Several numerical tests for two-dimensional problems show that the method is stable, accurate, and robust. This paper is an interesting example of how the traditional differencing technique combined with a good mathematical insight can lead to efficient schemes for domains with complex shape.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1036507
zbMATH Keywords: stability
zbMATH Keywords: fourth-order accurate
zbMATH Keywords: finite difference scheme
zbMATH Keywords: diffusion equation
zbMATH Keywords: domain with complex shape
zbMATH Keywords: numerical tests
reviewed by: Raytcho D. Lazarov
MaRDI profile type: Publication
OpenAlex ID: W2093132693
cites work: Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
cites work: Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II
DOI: 10.1006/JCPH.1997.5653
description: scientific article; zbMATH DE number 1036507