Equilibrated residual error estimator for edge elements
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- by Dietrich Braess and Joachim Schöberl PDF
- Math. Comp. 77 (2008), 651-672 Request permission
Abstract:
Reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem. A cheap computation of such functions via equilibration is well known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to the curl-curl equation and edge elements. The construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions. For this reason, Raviart–Thomas elements are extended in the spirit of distributions.References
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Additional Information
- Dietrich Braess
- Affiliation: Faculty of Mathematics, Ruhr-University, D 44780 Bochum, Germany
- Email: Dietrich.Braess@rub.de
- Joachim Schöberl
- Affiliation: Center for Computational Engineering Science, RWTH Aachen University, D 52062 Aachen, Germany
- Email: joachim.schoeberl@mathcces.rwth-aachen.de
- Received by editor(s): July 26, 2006
- Received by editor(s) in revised form: February 20, 2007
- Published electronically: November 20, 2007
- Additional Notes: The second author acknowledges support from the Austrian Science Foundation FWF within project grant Start Y-192, “hp-FEM: Fast Solvers and Adaptivity”
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 651-672
- MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-07-02080-7
- MathSciNet review: 2373174