Paper Info
Title
Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
Abstract
A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter epsilon(2) is arbitrarily small, which induces boundary layers. Constructing discrete sub-and super-solutions, we prove existence and investigate the accuracy of multiple discrete solutions on layer-adapted meshes of Bakhvalov and Shishkin types. It is shown that one gets second-order convergence (with, in the case of the Shishkin mesh, a logarithmic factor) in the discrete maximum norm, uniformly in epsilon for epsilon <= Ch. Here h > 0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch(-2). Numerical experiments are performed to support the theoretical results.
Year
DOI
Venue
2007
10.1090/S0025-5718-06-01938-7
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
semilinear reaction-diffusion,singular perturbation,maximum norm error estimate,Z-field,Bakhvalov mesh,Shishkin mesh,second order
Convergence (routing),Mathematical optimization,Polygon mesh,Mathematical analysis,Singular perturbation,Boundary layer,Logarithm,Numerical analysis,Reaction–diffusion system,Mathematics,Diffusion equation
Journal
Volume
Issue
ISSN
76
258
0025-5718
Citations 
PageRank 
References 
7
1.40
2
Authors
1
Name
Order
Citations
PageRank
Natalia Kopteva113022.08