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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
69/2005

Asymptotically Exact Functional Error Estimators Based on Superconvergent Gradient Recovery

Jeffrey Ovall

Abstract

The use of dual/adjoint problems for approximating functionals of solutions of PDEs with great accuracy or to merely drive a goal-oriented adaptive refinement scheme has become well-accepted, and it continues to be an active area of research. The traditional approach involves dual residual weighting (DRW). In this work we present two new functional error estimators and give conditions under which we can expect them to be asymptotically exact. The first is of DRW type and is derived for meshes in which most triangles satisfy an $\cO(h^2)$-approximate parallelogram property. The second functional estimator involves dual error estimate weighting (DEW) using any superconvergent gradient recovery technique for the primal and dual solutions. Several experiments are done which demonstrate the asymptotic exactness of a DEW estimator which uses a gradient recovery scheme proposed by Bank and Xu, and the effectiveness of refinement done with respect to the corresponding local error indicators.

Received:
Jun 30, 2005
Published:
Jun 30, 2005
MSC Codes:
49N15, 65N15, 65N30, 65N50
Keywords:
duality, finite elements, goal-oriented refinement

Related publications

inJournal
2006 Repository Open Access
Jeffrey S. Ovall

Asymptotically exact functional error estimators based on superconvergent gradient recovery

In: Numerische Mathematik, 102 (2006) 3, pp. 543-558