L2-STABILITY INDEPENDENT OF DIFFUSION FOR A FINITE ELEMENT-FINITE VOLUME DISCRETIZATION OF A LINEAR CONVECTION-DIFFUSION EQUATION

被引：12

作者：

Deuring, Paul ^{[1
,2
]}

Eymard, Robert ^{[3
]}

Mildner, Marcus ^{[1
,2
]}

机构：

[1] Univ Lille Nord France, F-59000 Lille, France

[2] ULCO, LMPA, F-62228 Calais, France

[3] Univ Paris Est Marne la Vallee, F-77454 Marne La Vallee, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2015年 / 53卷 / 01期

关键词：

convection-diffusion equation; combined finite element-finite volume method; Crouzeix-Raviart finite elements; barycentric finite volumes; upwind method; stability; POINCARE-FRIEDRICHS INEQUALITIES; SCHEME; CONVERGENCE; STABILIZATION; FLOWS; H-1;

D O I：

10.1137/140961146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element-finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is shown to be unconditionally L-2-stable, uniformly with respect to the diffusion coefficient.

引用

页码：508 / 526

页数：19

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