Dual-mixed finite element approximation of Stokes and nonlinear Stokes problems using trace-free velocity gradients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Howell, Jason S.

关键词: Stokes problem;    Nonlinear Stokes problem;    Dual-mixed method;    Finite element method;    Twofold saddle point problem;    Raviart-Thomas;    Pseudostress;   

DOI  :  10.1016/j.cam.2009.05.002

来源: Elsevier

【 摘 要 】

In this work a finite element method for a dual-mixed approximation of Stokes and nonlinear Stokes problems is studied. The dual-mixed structure, which yields a twofold saddle point problem, arises in a formulation of this problem through the introduction Of unknown variables with relevant physical meaning. The method approximates the velocity, its gradient, and the total stress tensor, but avoids the explicit computation of the pressure, which can be recovered through a simple postprocessing technique. This method improves an existing approach for these problems and uses Raviart-Thomas elements and discontinuous piecewise polynomials for approximating the unknowns. Existence, uniqueness, and error results for the method are given, and numerical experiments that exhibit the reduced computational cost of this approach are presented. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free