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UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS.

Authors :
Xiaoping Xie
Jinchao Xu
Guangri Xue
Source :
Journal of Computational Mathematics. May2008, Vol. 26 Issue 3, p437-455. 19p.
Publication Year :
2008

Abstract

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that tremors both Darcy's law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zeroth-order term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods are based on the original weak formulations of Darcy-Stokes-Brinkman equations. In the first method we consider the existing Stokes elements. We show that a stable Stokes element is also uniformly stable with respect to the coefficients and the jumps of Darcy-Stokes-Brinkman equations if and only if the discretely divergence-free velocity implies almost everywhere divergence-free one. In the second method we construct uniformly stable elements by modifying some well-known H(div)-conforming elements. We give some new 2D and 3D elements in a unified way. In the last method we modify the original weak formulation of Darcy-Stokes-Brinkman equations with a stabilization term. We show that all traditional stable Stokes elements are uniformly stable with respect to the coefficients and their jumps under this new formulation. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02549409
Volume :
26
Issue :
3
Database :
Academic Search Index
Journal :
Journal of Computational Mathematics
Publication Type :
Academic Journal
Accession number :
36382719