Approximation of generalized Stokes problems using dual-mixed finite elements without enrichment

作者：Howell Jason S^*

来源：International Journal for Numerical Methods in Fluids, 2011, 67(2): 247-268.

DOI：10.1002/fld.2356

• Stokes problem
• generalized Stokes problem
• twofold saddle point problem
• Raviart-Thomas
• pseudostress
• finite element method
• dual-mixed method

In this work a finite element method for a dual-mixed approximation of generalized Stokes problems in two or three space dimensions is studied. A variational formulation of the generalized Stokes problems is accomplished through the introduction of the pseudostress and the trace-free velocity gradient as unknowns, yielding a twofold saddle point problem. The method avoids the explicit computation of the pressure, which can be recovered through a simple post-processing technique. Compared with an existing approach for the same problem, the method presented here reduces the global number of degrees of freedom by up to one-third in two space dimensions. The method presented here also represents a connection between existing dual-mixed and pseudostress methods for Stokes problems. Existence, uniqueness, and error results for the generalized Stokes problems are given, and numerical experiments that illustrate the theoretical results are presented.

• 出版日期2011-9-20