A Numerical Study of Uniform Superconvergence of LDG Method for Solving Singularly Perturbed Problems
Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 280–298
Abstract
In this paper, we consider the local discontinuous Galerkin method (LDG) for solving singularly perturbed convection-diffusion problems in one- and two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementation of two-type different anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform 2p+1-order superconvergence is observed numerically for both one-dimensional and two-dimensional cases.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-JCM-8573
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 280–298
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence.