Optimal convergence of the original dg method for the transport-reaction equation on special meshes

被引：79

作者：

Cockburn, Bernardo ^{[1
]}

Dong, Bo ^{[1
]}

Guzman, Johnny ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 03期

关键词：

discontinuous Galerkin methods; transport; reaction equation; error estimates;

D O I：

10.1137/060677215

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the approximation given by the original discontinuous Galerkin method for the transport-reaction equation in d space dimensions is optimal provided the meshes are suitably chosen: the L(2)-norm of the error is of order k + 1 when the method uses polynomials of degree k. These meshes are not necessarily conforming and do not satisfy any uniformity condition; they are required only to be made of simplexes, each of which has a unique outflow face. We also find a new, element-by-element postprocessing of the derivative in the direction of the flow which superconverges with order k + 1.

引用

页码：1250 / 1265

页数：16

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