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New approaches to error estimation and adaptivity for the Stokes and Oseen equations
Author(s) -
Oden J.T.,
Prudhomme S.
Publication year - 1999
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/(sici)1097-0363(19990915)31:1<3::aid-fld952>3.0.co;2-b
Subject(s) - a priori and a posteriori , estimator , mathematics , norm (philosophy) , residual , finite element method , stokes flow , mathematical optimization , boundary (topology) , computer science , mathematical analysis , algorithm , geometry , flow (mathematics) , physics , philosophy , statistics , epistemology , political science , law , thermodynamics
We present a new approach to deliver reliable approximations of the norm of the residuals resulting from finite element solutions to the Stokes and Oseen equations. The method is based upon a global solve in a bubble space using iterative techniques. This provides an alternative to the classical equilibrated element residual methods for which it is necessary to construct proper boundary conditions for each local problem. The method is first used to develop a global a posteriori error estimator. It is then applied in a strategy to control the numerical error in specific outputs or quantities of interest which are functions of the solutions to the Stokes and Oseen equations. Copyright © 1999 John Wiley & Sons, Ltd.