Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

Natalia Kopteva

doi:10.1093/imanum/drl020

Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

Natalia Kopteva

Research output: Contribution to journal › Article › peer-review

Abstract

A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.

Original language	English
Pages (from-to)	576-592
Number of pages	17
Journal	IMA Journal of Numerical Analysis
Volume	27
Issue number	3
DOIs	https://doi.org/10.1093/imanum/drl020
Publication status	Published - Jul 2007

Keywords

A posteriori error estimate
Finite differences
Grid equidistribution
Layer-adapted mesh
Maximum norm
Reaction-diffusion
Singular perturbation

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10.1093/imanum/drl020

Cite this

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title = "Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem",

abstract = "A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.",

keywords = "A posteriori error estimate, Finite differences, Grid equidistribution, Layer-adapted mesh, Maximum norm, Reaction-diffusion, Singular perturbation",

author = "Natalia Kopteva",

year = "2007",

month = jul,

doi = "10.1093/imanum/drl020",

language = "English",

volume = "27",

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journal = "IMA Journal of Numerical Analysis",

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AU - Kopteva, Natalia

PY - 2007/7

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N2 - A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.

AB - A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.

KW - A posteriori error estimate

KW - Finite differences

KW - Grid equidistribution

KW - Layer-adapted mesh

KW - Maximum norm

KW - Reaction-diffusion

KW - Singular perturbation

UR - https://www.scopus.com/pages/publications/34547796809

U2 - 10.1093/imanum/drl020

DO - 10.1093/imanum/drl020

M3 - Article

AN - SCOPUS:34547796809

SN - 0272-4979

VL - 27

SP - 576

EP - 592

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 3

ER -

Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

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Keywords

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