000180351 001__ 180351
000180351 005__ 20190316235443.0
000180351 037__ $$aARTICLE
000180351 245__ $$aA posteriori error estimates for the finite element approximation of the Stokes problem
000180351 269__ $$a2003
000180351 260__ $$c2003
000180351 336__ $$aJournal Articles
000180351 520__ $$aIn this paper we propose a new technique to obtain upper and lower bounds on the energy norm of the error in the velocity field, for the Stokes problem. It relies on a splitting of the velocity error in two contributions: a projection error, that quantifies the distance of the computed solution to the space of divergence free functions, and an error in satisfying the momentum equation. We will show that both terms can be sharply estimated, from above and from below, by implicit a posteriori error estimators. In particular, the proposed estimator is based on the solution of local Stokes problems both with “Neumann-type” boundary conditions, extending the ideas presented in [12, 17] for the Laplace equation, and homogeneous Dirichlet boundary conditions. The numerical results show very good effectivity indices. The underlying idea is quite general and can be applied to other saddle point problems as well, as the ones arising in mixed formulations of second order PDEs.
000180351 6531_ $$alower bounds
000180351 6531_ $$aerror in the velocity field
000180351 6531_ $$aStokes problem
000180351 6531_ $$asplitting of the velocity error
000180351 6531_ $$aprojection error
000180351 6531_ $$aspace of divergence
000180351 6531_ $$aerror in satisfying the momentum
000180351 700__ $$g118353$$aNobile, Fabio$$0241873
000180351 773__ $$tTICAM Report 03-13
000180351 8564_ $$uhttp://www.ices.utexas.edu/research/reports/4/?yearFilter=2003&keywordQuery=$$zURL
000180351 8564_ $$uhttps://infoscience.epfl.ch/record/180351/files/A_posteriori_error_estimates.pdf$$zn/a$$s436511$$yn/a
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000180351 917Z8 $$x178574
000180351 917Z8 $$x118353
000180351 937__ $$aEPFL-ARTICLE-180351
000180351 973__ $$rNON-REVIEWED$$sPUBLISHED$$aOTHER
000180351 980__ $$aARTICLE