Pseudostress-BasedMixed Finite Element Methods for the Stokes Problem in Rn with Dirichlet Boundary Conditions.I:A Priori Error Analysis
作者机构：CI2MA and Departamento de Ingenier´ıa Matem´aticaUniversidad de Concepci´onCasilla 160-CConcepcionChile Departamento de Construcci´on e Ingenier´ıa de FabricacionUniversidad de OviedoOviedoEspa-na.
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2012年第12卷第6期
页 面：109-134页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Mixed finite element pseudostress incompressible flow
摘 要：We consider a non-standard mixed method for the Stokes problem in Rn,n∈{2,3},with Dirichlet boundary conditions,in which,after using the incompressibility condition to eliminate the pressure,the pseudostress tensor s and the velocity vector u become the only ***,we apply the Babuˇska-Brezzi theory to prove the well-posedness of the corresponding continuous and discrete *** particular,we show that Raviart-Thomas elements of order k≥0 for s and piecewise polynomials of degree k for u ensure unique solvability and stability of the associated Galerkin *** addition,we introduce and analyze an augmented approach for our pseudostress-velocity *** methodology employed is based on the introduction of the Galerkin least-squares type terms arising from the constitutive and equilibrium equations,and the Dirichlet boundary condition for the velocity,all of them multiplied by suitable stabilization *** show that these parameters can be chosen so that the resulting augmented variational formulation is defined by a strongly coercive bilinear form,whence the associated Galerkin scheme becomes well posed for any choice of finite element *** instance,Raviart-Thomas elements of order k≥0 for s and continuous piecewise polynomials of degree k+1 for u become a feasible choice in this ***,extensive numerical experiments illustrating the good performance of the methods and comparing them with other procedures available in the literature,are provided.
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