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Mathematics of Computation

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Equilibrated residual error estimator for edge elements


Authors: Dietrich Braess and Joachim Schöberl
Journal: Math. Comp. 77 (2008), 651-672
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-07-02080-7
Published electronically: November 20, 2007
MathSciNet review: 2373174
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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.


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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

DOI: https://doi.org/10.1090/S0025-5718-07-02080-7
Keywords: A posteriori error estimates, Maxwell equations
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”
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.