Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem

Natalia Kopteva

doi:10.1137/060677616

Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem

Natalia Kopteva

Mathematics And Statistics

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32 Citations (Scopus)

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Abstract

A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate

Original language	English
Pages (from-to)	1602-1618
Number of pages	17
Journal	SIAM Journal on Numerical Analysis
Volume	46
Issue number	3
DOIs	https://doi.org/10.1137/060677616
Publication status	Published - 11 Apr 2008

Keywords

reaction-diffusion
singular perturbation
a posteriori error estimate
maximum norm
no mesh aspect ratio condition
finite differences
layer-adapted mesh

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10.1137/060677616

060677616Submitted manuscript, 226 KB

Cite this

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title = "Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem",

abstract = "A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate ",

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AB - A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimate

KW - reaction-diffusion

KW - singular perturbation

KW - a posteriori error estimate

KW - maximum norm

KW - no mesh aspect ratio condition

KW - finite differences

KW - layer-adapted mesh

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DO - 10.1137/060677616

M3 - Article

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 3

ER -

Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem

Abstract

Keywords

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