A stable enriched Galerkin element for the Stokes problem

被引：12

作者：

Chaabane, Nabil ^{[1
]}

Girault, Vivette ^{[1
,2
]}

Riviere, Beatrice ^{[1
]}

Thompson, Travis ^{[1
]}

机构：

[1] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA

[2] UPMC Univ Paris 06, Lab Jacques Louis Lions, CNRS, Sorbonne Univ,UMR 7598, Paris, France

来源：

APPLIED NUMERICAL MATHEMATICS | 2018年 / 132卷

关键词：

inf-sup condition; Enriched Galerkin; Stabilized divergence operator; Fortin's Lemma; Local mass conservation; Error estimates; STATIONARY STOKES; FINITE-ELEMENTS; DIVERGENCE; EQUATIONS; INTERPOLATION; REGULARITY; STABILITY; OPERATOR;

D O I：

10.1016/j.apnum.2018.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a stable element for the divergence operator that approximates the velocity by continuous linear polynomials plus piecewise constants and the pressure by piecewise constants. A uniform inf-sup condition is obtained for conforming meshes in two or three dimensions. The resulting method belongs to the class of enriched Galerkin methods, and is applied to the solution of a Stokes system. A priori error estimates in the energy norm and in the L-2 norm are derived. Extensions to the Navier-Stokes system are presented. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1 / 21

页数：21

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