Unilateral problem for the Stokes equations: The well-posedness and finite element approximation

被引：13

作者：

Saito, Norikazu ^{[1
]}

Sugitani, Yoshiki ^{[1
]}

Zhou, Guanyu ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

来源：

APPLIED NUMERICAL MATHEMATICS | 2016年 / 105卷

关键词：

Stokes equations; Finite element approximation; Unilateral boundary condition; BOUNDARY-CONDITIONS; L2-PROJECTION; STABILITY;

D O I：

10.1016/j.apnum.2016.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the stationary Stokes equations under a unilateral boundary condition of Signorini's type, which is one of artificial boundary conditions in flow problems. Well-posedness is discussed through its variational inequality formulation. We also consider the finite element approximation for a regularized penalty problem. The well-posedness, stability and error estimates of optimal order are established. The lack of a coupled Babuska and Brezzi's condition makes analysis difficult. We offer a new method of analysis. Particularly, our device to treat the pressure is novel and of some interest. Numerical examples are presented to validate our theoretical results. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：124 / 147

页数：24

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