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

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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 - 2008

Keywords

A posteriori error estimate
Finite differences
Layer-adapted mesh
Maximum norm
No mesh aspect ratio condition
Reaction-diffusion
Singular perturbation

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10.1137/060677616

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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.",

keywords = "A posteriori error estimate, Finite differences, Layer-adapted mesh, Maximum norm, No mesh aspect ratio condition, Reaction-diffusion, Singular perturbation",

author = "Natalia Kopteva",

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AU - Kopteva, Natalia

PY - 2008

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N2 - 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.

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 - A posteriori error estimate

KW - Finite differences

KW - Layer-adapted mesh

KW - Maximum norm

KW - No mesh aspect ratio condition

KW - Reaction-diffusion

KW - Singular perturbation

UR - https://www.scopus.com/pages/publications/55349138107

U2 - 10.1137/060677616

DO - 10.1137/060677616

M3 - Article

AN - SCOPUS:55349138107

SN - 0036-1429

VL - 46

SP - 1602

EP - 1618

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

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