Paper Info
Title
Numerical 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 ε 2 is arbitrarily small, which induces boundary layers. We extend the numerical method and its maximum norm error analysis of the paper [N. Kopteva: Math. Comp. 76 (2007) 631–646], in which a parametrization of the boundary $\partial\Omega$ is assumed to be known, to a more practical case when the domain is defined by an ordered set of boundary points. It is shown that, using layer-adapted meshes, one gets second-order convergence in the discrete maximum norm, uniformly in ε for ε ≤ Ch. Here h  0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch − 2. Numerical results are presented that support our theoretical error estimates.
Year
DOI
Venue
2008
10.1007/978-3-642-00464-3_8
NAA
Keywords
Field
DocType
singularly perturbed semilinear reaction-diffusion,numerical analysis,boundary point,numerical method,mesh element,maximum side length,mesh node,layer-adapted mesh,numerical result,discrete maximum norm,maximum norm error analysis,boundary layer,reaction diffusion,second order
Convergence (routing),Ordered set,Polygon mesh,Parametrization,Mathematical analysis,Mesh node,Numerical analysis,Reaction–diffusion system,Mathematics
Conference
Volume
ISSN
Citations 
5434
0302-9743
2
PageRank 
References 
Authors
0.44
2
1
Name
Order
Citations
PageRank
Natalia Kopteva113022.08