A mixed finite element method for the generalized Stokes problem
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A mixed finite element method for the generalized Stokes problemData
2005-08-03Cita bibliográfica
Bustinza, R., G. N. Gatica, M. González. A mixed finite element method for the generalized Stokes problem. International Journal for Numerical Methods in Fluids, Nov 2005; 49(8): 877-903.
Resumo
[Abstract] We present and analyse a new mixed finite element method for the generalized Stokes problem. The approach, which is a natural extension of a previous procedure applied to quasi-Newtonian Stokes flows, is based on the introduction of the flux and the tensor gradient of the velocity as further unknowns. This yields a two-fold saddle point operator equation as the resulting variational formulation. Then, applying a slight generalization of the well known Babuška–Brezzi theory, we prove that the continuous and discrete formulations are well posed, and derive the associated a priori error analysis. In particular, the finite element subspaces providing stability coincide with those employed for the usual Stokes flows except for one of them that needs to be suitably enriched. We also develop an a posteriori error estimate (based on local problems) and propose the associated adaptive algorithm to compute the finite element solutions. Several numerical results illustrate the performance of the method and its capability to localize boundary layers, inner layers, and singularities.
Palabras chave
Mixed finite element
Stokes problem
A priori error estimate
A posteriori error estimate
Stokes problem
A priori error estimate
A posteriori error estimate
Dereitos
This is the peer reviewed version of the following article: Bustinza, R., G. N. Gatica, M. González. A mixed finite element method for the generalized Stokes problem. International Journal for Numerical Methods in Fluids, Nov 2005; 49(8): 877-903, which has been published in final form at http://dx.doi.org/ 10.1002/fld.1029. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
ISSN
0271-2091
1097-0363
1097-0363