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A stabilized finite element method for the Stokes problem based on polynomial pressure projections
Author(s) -
Dohrmann Clark R.,
Bochev Pavel B.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.752
Subject(s) - finite element method , mathematics , mixed finite element method , polynomial , simple (philosophy) , extended finite element method , affine transformation , navier–stokes equations , minification , mathematical analysis , element (criminal law) , mathematical optimization , geometry , physics , compressibility , mechanics , philosophy , epistemology , political science , law , thermodynamics
A new stabilized finite element method for the Stokes problem is presented. The method is obtained by modification of the mixed variational equation by using local L 2 polynomial pressure projections. Our stabilization approach is motivated by the inherent inconsistency of equal‐order approximations for the Stokes equations, which leads to an unstable mixed finite element method. Application of pressure projections in conjunction with minimization of the pressure–velocity mismatch eliminates this inconsistency and leads to a stable variational formulation. Unlike other stabilization methods, the present approach does not require specification of a stabilization parameter or calculation of higher‐order derivatives, and always leads to a symmetric linear system. The new method can be implemented at the element level and for affine families of finite elements on simplicial grids it reduces to a simple modification of the weak continuity equation. Numerical results are presented for a variety of equal‐order continuous velocity and pressure elements in two and three dimensions. Copyright © 2004 John Wiley & Sons, Ltd.