This article is dealt with the study of a hybrid numerical scheme for a class of singularly perturbed mixed parabolic-elliptic problems possessing both boundary and interior layers. The domain under consideration is partitioned into two subdomains. In the first subdomain, the given problem takes the form of parabolic reaction-diffusion type, whereas in the second subdomain elliptic convection-diffusion-reaction types of problems are posed. To solve these problems, the time derivative is discretized by the backward-Euler method, while for the spatial discretization the classical central difference scheme is used on the first subdomain and a hybrid finite difference scheme is proposed on the second subdomain. The proposed method is designed on a layer resolving piecewise-uniform Shishkin mesh and computationally it is shown that the method converges ε-uniformly with almost second-order spatial accuracy in the discrete supremum norm. © 2013 Springer-Verlag.
CITATION STYLE
Mukherjee, K., & Natesan, S. (2013). An efficient hybrid numerical scheme for singularly perturbed problems of mixed parabolic-elliptic type. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8236 LNCS, pp. 411–419). https://doi.org/10.1007/978-3-642-41515-9_46
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