Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh
Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 845–859
Abstract
In this paper, we introduce a coupled approach of local discontinuous Galerkin (LDG) and continuous finite element method (CFEM) for solving singularly perturbed convection-diffusion problems. When the coupled continuous-discontinuous linear FEM is used under the Shishkin mesh, a uniform convergence rate O(N−1lnN) in an associated norm is established, where N is the number of elements. Numerical experiments complement the theoretical results. Moreover, a uniform convergence rate O(N−2) in L2 norm, is observed numerically on the Shishkin mesh.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-599
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 845–859
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: convection diffusion equation local discontinuous Galerkin method finite element method Shishkin mesh uniform convergence.