Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem
Year: 2018
Author: Yao Cheng, Qiang Zhang, Haijin Wang
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 6 : pp. 785–810
Abstract
In this paper, we analyze the local discontinuous Galerkin method with the generalized alternating numerical flux for two-dimensional singularly perturbed problem with outflow boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy technique with suitable weight function, we obtain the double-optimal error estimate, namely, the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12609
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 6 : pp. 785–810
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Local analysis local discontinuous Galerkin method generalized alternating numerical flux error estimate singularly perturbed problem.