A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an \(L\)-shaped domain

DOI10.3103/S0278641912030028zbMath1258.65077OpenAlexW2166689321MaRDI QIDQ1759155

T. Ya. Ershova

Publication date: 20 November 2012

Published in: Moscow University Computational Mathematics and Cybernetics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0278641912030028

zbMATH Keywords

numerical examplesingular perturbationuniform convergencemixed boundary conditionscorner singularitiesShishkin meshreaction-diffusion equation\(L\)-shaped domainfive-point difference scheme

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Cites Work

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• Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an $L$-shaped domain
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square

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