Numerical solution of a mixed singularly perturbed parabolic-elliptic problem

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:320

Article

Brayanov, Iliya A.

关键词: parabolic-elliptic problems;    convection-diffusion problems;    singular perturbation;    asymptotic analysis;    finite volume methods;    modified upwind approximations;    uniform convergence;    Shishkin mesh;   

DOI  :  10.1016/j.jmaa.2005.06.098

来源: Elsevier

【 摘 要 】

A one-dimensional singularly perturbed problem of mixed type is considered. The domain under consideration is partitioned into two subdomains. In the first subdomain a parabolic reaction-diffusion problem is given and in the second one an elliptic convection-diffusion-reaction problem. The solution is decomposed into regular and singular components. The problem is discretized using an inverse-monotone finite volume method on condensed Shishkin meshes. We establish an almost second-order global pointwise convergence in the space variable, that is uniform with respect to the perturbation parameter. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free