A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an \(L\)-shaped domain. (English. Russian original) Zbl 1258.65077
Mosc. Univ. Comput. Math. Cybern. 36, No. 3, 109-119 (2012); translation from Vestn. Mosk. Univ., Ser. XV 2012, No. 3, 3-12 (2012).
A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an \(L\)-shaped domain is considered for when the solution has singularities at the corners of the domain. The densification of the Shishkin mesh near the inner corner where different boundary conditions meet is such that the solution obtained by the classical five-point difference scheme converges to the solution of the initial problem in the mesh norm \(L_\infty^h\) uniformly with respect to the small parameter with almost second order. Numerical modeling of a particular problem is presented to confirm the theoretical results.
Reviewer: T. C. Mohan (Dehra Dun)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35B25 | Singular perturbations in context of PDEs |
Keywords:
reaction-diffusion equation; singular perturbation; corner singularities; \(L\)-shaped domain; mixed boundary conditions; uniform convergence; numerical example; Shishkin mesh; five-point difference schemeReferences:
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