Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem

DOI10.1090/S0025-5718-06-01938-7zbMath1113.65100MaRDI QIDQ3426017

Natalia Kopteva

Publication date: 7 March 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

convergencesingular perturbationnumerical examplesmultiple solutionsboundary layersBakhvalov meshShishkin meshsupersolutionssubsolutionssemilinear reaction-diffusion problemsmaximum norm error estimates

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

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Cites Work

• Semilinear elliptic boundary value problems with small parameters
• \(hp\)-finite element methods for singular perturbations
• Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• A uniformly convergent method for a singularly perturbed semilinear reaction–diffusion problem with multiple solutions
• A parameter robust numerical method for a two dimensional reaction-diffusion problem
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