Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem

Natalia Kopteva; Torsten Linß

doi:10.2478/cmam-2012-0013

Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem

Natalia Kopteva, Torsten Linß

Department of Mathematics and Statistics

FernUniversität in Hagen

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

Abstract

A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L ₁-norm bounds for the Green's function of the parabolic operator and its derivatives are derived that form the basis of the a posteriori error analysis. Numerical results are presented.

Original language	English
Pages (from-to)	189-205
Number of pages	17
Journal	Computational Methods in Applied Mathematics
Volume	12
Issue number	2
DOIs	https://doi.org/10.2478/cmam-2012-0013
Publication status	Published - Apr 2012

Keywords

A posteriori error estimate
Backward-Euler
Maximum norm
Parabolic equations
Reaction-diffusion
Singular perturbation

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10.2478/cmam-2012-0013

Cite this

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abstract = "A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L 1-norm bounds for the Green's function of the parabolic operator and its derivatives are derived that form the basis of the a posteriori error analysis. Numerical results are presented.",

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AB - A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L 1-norm bounds for the Green's function of the parabolic operator and its derivatives are derived that form the basis of the a posteriori error analysis. Numerical results are presented.

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KW - Maximum norm

KW - Parabolic equations

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KW - Singular perturbation

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Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem

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Keywords

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