Equilibrated error estimators for discontinuous Galerkin methods

Sarah Cochez‐Dhondt; Serge Nicaise

doi:10.1002/num.20315

journal article Jul 21, 2008

Equilibrated error estimators for discontinuous Galerkin methods

Sarah Cochez‐Dhondt Serge Nicaise

Numerical Methods for Partial Differential Equations Vol. 24 No. 5 pp. 1236-1252 · Wiley

View at Publisher Save 10.1002/num.20315

Abstract

AbstractWe consider some diffusion problems in domains of ℝd, d = 2 or 3 approximated by a discontinuous Galerkin method with polynomials of any degree. We propose a new a posteriori error estimator based on H(div)‐conforming elements. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. The lower bound is also established with a constant depending on the aspect ratio of the mesh, the dependence with respect to the coefficients being also traced. The reliability and efficiency of the proposed estimator is confirmed by some numerical tests. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

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Metrics

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Citations

28

References

Details

Published: Jul 21, 2008
Vol/Issue: 24(5)
Pages: 1236-1252
License: View

Authors

Laboratoire de Mathématiques et leurs Applications, Université Polytechnique des Hauts-de-France, Valenciennes, France

Cite This Article

Sarah Cochez‐Dhondt, Serge Nicaise (2008). Equilibrated error estimators for discontinuous Galerkin methods. Numerical Methods for Partial Differential Equations, 24(5), 1236-1252. https://doi.org/10.1002/num.20315

Equilibrated error estimators for discontinuous Galerkin methods

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