Error estimates for finite element methods for scalar conservation laws

被引：73

作者：

Cockburn, B

Gremaud, PA

机构：

[1] School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis

[2] Department of Mathematics, North Carolina State University, Box 8205, Raleigh

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1996年 / 33卷 / 02期

关键词：

error estimates; streamline diffusion method; discontinuous galerkin method; multidimensional conservation laws;

D O I：

10.1137/0733028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, new a posteriori error estimates for the shock-capturing streamline diffusion (SCSD) method and the shock-capturing discontinuous galerkin (SCDG) method for scalar conservation laws are obtained. These estimates are then used to prove that the SCSD method and the SCDG method converge to the entropy solution with a rate of at least h(1/8) and h(1/4), respectively, in the L(infinity)(L(1))-norm. The triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k. The result is independent of the dimension of the space.

引用

页码：522 / 554

页数：33

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