Approximation of singularly perturbed reaction-diffusion equations on adaptive grids (Q2734693)
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scientific article; zbMATH DE number 1635795
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of singularly perturbed reaction-diffusion equations on adaptive grids |
scientific article; zbMATH DE number 1635795 |
Statements
24 March 2003
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difference methods
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reaction-diffusion equations
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singular parameter
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singular perturbation
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error bounds
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mesh refinement
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Approximation of singularly perturbed reaction-diffusion equations on adaptive grids (English)
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The nonstationary reaction-diffusion equation with one space variable is considered with standard initial and Dirichlet conditions. It is well known that the presence of the singular parameter makes one to apply difference approximations with special attention to construction of grids. The author applies a natural refinement procedure with uniformgrids on subdomains that are found on the base of a posteriori analyses of the gradient of intermediate solutions. Estimates of errors are given that lead to relatively small influence of the singular parameter (under additional assumptions on the solution).
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