An adaptive algorithm for the Stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio

An adaptive algorithm is proposed for solving the Stokes problem with continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Anisotropic, a posteriori error estimates in the H-1 x L-2 norm are derived, the constant being independent from the mesh aspect ratio. The estimates involve the first derivatives of the velocity error and the velocity of a dual problem having the pressure error in the right side. An explicit error indicator is then proposed. The first derivatives of the velocity error are approximated using Zienkiewicz-Zhu error estimator (post-processing). The pressure error in the right side of the dual problem is approximated by smoothing. Numerical results on meshes with large aspect ratio show that the error indicator is robust whenever the pressure error in the dual problem is approximated with sufficient accuracy. Finally, an adaptive algorithm is proposed, with goal to build an anisotropic triangulation such that the relative estimated error is close to a preset tolerance. (c) 2004 IMACS. Published by Elsevier B.V. All rights reserved.


Published in:
Applied Numerical Mathematics, 54, 3-4, 470-490
Year:
2005
ISSN:
0168-9274
Keywords:
Note:
Ecole Polytech Fed Lausanne, Fac Sci Base, Inst Anal & Calcul Sci, CH-1015 Lausanne, Switzerland. Picasso, M, Ecole Polytech Fed Lausanne, Fac Sci Base, Inst Anal & Calcul Sci, Batiment Math, CH-1015 Lausanne, Switzerland. macro.picasso@epfl.ch
ISI Document Delivery No.: 942XV
Times Cited: 0
Cited Reference Count: 42
Other identifiers:
Laboratories:




 Record created 2006-08-24, last modified 2018-03-17


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