Dual-mixed finite element approximation of Stokes and nonlinear Stokes problems using trace-free velocity gradients
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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.
论文关键词:65N Except 65N06,65N12,65N15,65N40,Stokes problem,Nonlinear Stokes problem,Dual-mixed method,Finite element method,Twofold saddle point problem,Raviart–Thomas,Pseudostress
论文评审过程:Received 10 February 2009, Revised 20 April 2009, Available online 9 May 2009.
论文官网地址:https://doi.org/10.1016/j.cam.2009.05.002