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- W1800410760 abstract "A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter ε 2 is arbitrarily small, which induces boundary layers. We extend the numerical method and its maximum norm error analysis of the paper [N. Kopteva: Math. Comp. 76 (2007) 631–646], in which a parametrization of the boundary (partialOmega) is assumed to be known, to a more practical case when the domain is defined by an ordered set of boundary points. It is shown that, using layer-adapted meshes, one gets second-order convergence in the discrete maximum norm, uniformly in ε for ε ≤ Ch. Here h > 0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch − 2. Numerical results are presented that support our theoretical error estimates.KeywordsMesh NodePolygonal DomainSingularly PerturbShishkin MeshApproximate CurvatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W1800410760 created "2016-06-24" @default.
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- W1800410760 date "2009-01-01" @default.
- W1800410760 modified "2023-09-27" @default.
- W1800410760 title "Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem" @default.
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- W1800410760 doi "https://doi.org/10.1007/978-3-642-00464-3_8" @default.
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