Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem

Natalia Kopteva

doi:10.1137/S0036142900368642

Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem

Natalia Kopteva

Lomonosov Moscow State University

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

Abstract

A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first- and second-order difference schemes, including upwind schemes. We give first- and second-order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter. Numerical experiments support the theoretical results.

Original language	English
Pages (from-to)	423-441
Number of pages	19
Journal	SIAM Journal on Numerical Analysis
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/S0036142900368642
Publication status	Published - 2002
Externally published	Yes

Keywords

A posteriori error estimate
Convection-diffusion
Finite difference scheme
Grid equidistribution
Layer-adapted mesh
Quasi-linear problem
Singular perturbation
Upwind scheme

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10.1137/S0036142900368642

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abstract = "A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first- and second-order difference schemes, including upwind schemes. We give first- and second-order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter. Numerical experiments support the theoretical results.",

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AB - A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first- and second-order difference schemes, including upwind schemes. We give first- and second-order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter. Numerical experiments support the theoretical results.

KW - A posteriori error estimate

KW - Convection-diffusion

KW - Finite difference scheme

KW - Grid equidistribution

KW - Layer-adapted mesh

KW - Quasi-linear problem

KW - Singular perturbation

KW - Upwind scheme

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EP - 441

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 2

ER -

Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem

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Keywords

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