Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem

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.

Author Details

Yao Cheng

Qiang Zhang

Haijin Wang