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UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS 被引量:23
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作者 Xiaoping Xie Jinchao Xu Guangri Xue 《Journal of Computational Mathematics》 SCIE EI CSCD 2008年第3期437-455,共19页
In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy's law and Stokes equations in a single form of PDE but with strongly disconti... In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy's law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder 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. 展开更多
关键词 Darcy-Stokes equation Brinkman Finite element Uniformly stable
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LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT METHODS FOR DARCY-STOKES PROBLEMS 被引量:7
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作者 Shiquan Zhang Xiaoping Xie Yumei Chen 《Journal of Computational Mathematics》 SCIE CSCD 2009年第2期400-424,共25页
In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and ... In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results. 展开更多
关键词 Darcy-Stokes problem Finite element Uniformly stable
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