Asymptotically exact functional error estimators based on superconvergent gradient recovery |
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Authors: | Jeffrey S Ovall |
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Institution: | (1) Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany |
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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 -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.
Resubmitted to Numerische Mathematik, June 30, 2005, with changes suggested by referees. |
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Keywords: | 49N15 65N15 65N30 65N50 |
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