Convergence of consistent and inconsistent finite difference schemes and an acceleration technique

Authors:
Tetsuro Yamamoto
Affiliations:
Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama, Japan
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

Citing 8
Cited 3

Numerical grid generation: foundations and applications

Numerical grid generation: foundations and applications
A simple adaptive grid method in two dimensions

SIAM Journal on Scientific Computing
The immersed interface method for elliptic equations with discontinuous coefficients and singular sources

SIAM Journal on Numerical Analysis
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

SIAM Journal on Scientific Computing
Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid

Journal of Computational and Applied Mathematics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation

SIAM Journal on Scientific Computing
Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence

Journal of Computational and Applied Mathematics
Superconvergence of the Shortley-Weller approximation for Dirichlet problems

Journal of Computational and Applied Mathematics

Convergence of finite difference methods for convection-diffusion problems with singular solutions

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Convergence analysis of adaptive finite difference methods using stretching functions for boundary value problems with singular solutions

Focus on computational neurobiology
Superconvergence of solution derivatives of the Shortley--Weller difference approximation to Poisson's equation with singularities on polygonal domains

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper states and generalizes in part some recent results on finite difference methods for Dirichlet problems in a bounded domain Ω which the author has obtained by himself or with coworkers. After stating a superconvergence property of finite difference solution for the case where the exact solution u belongs to C4(Ω), it is remarked that such a property does not hold in general if u ∉ C4(Ω). Next, a convergence theorem is given for inconsistent schemes under some assumptions. Furthermore, it is shown that the accuracy of the approximate solution can be improved by a coordinate transformation. Numerical examples are also given.