Volume 15, Issue 6
Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem

Yao Cheng ,  Qiang Zhang and Haijin Wang

Int. J. Numer. Anal. Mod., 15 (2018), pp. 785-810.

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  • 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 quasiuniform Cartesian meshes are used. Numerical experiments are given to verify the theoretical results.

  • History

Published online: 2018-08

  • AMS Subject Headings

65M12, 65M15, 65M60.

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