Local discontinuous Galerkin methods for the Stokes system

被引：224

作者：

Cockburn, B

Kanschat, G

Schotzau, D

Schwab, C

机构：

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

[2] Heidelberg Univ, Inst Angew Math, D-69120 Heidelberg, Germany

[3] ETHZ, Seminar Angew Math, CH-8092 Zurich, Switzerland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2002年 / 40卷 / 01期

关键词：

finite elements; discontinuous Galerkin methods; Stokes system;

D O I：

10.1137/S0036142900380121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For a class of shape regular meshes with hanging nodes we derive a priori estimates for the L-2-norm of the errors in the velocities and the pressure. We show that optimal-order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k-1 for the pressure, for any k greater than or equal to 1. We also consider the case in which all the unknowns are approximated with polynomials of degree k and show that, although the orders of convergence remain the same, the method is more efficient. Numerical experiments verifying these facts are displayed.

引用

页码：319 / 343

页数：25