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A goal‐oriented hp ‐adaptive discontinuous Galerkin approach for biharmonic problems
Author(s) -
Gonçalves João L.,
Gomes Sônia M.,
Devloo Philippe R.B.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4596
Subject(s) - biharmonic equation , estimator , benchmark (surveying) , discontinuous galerkin method , galerkin method , finite element method , mathematical optimization , mathematics , polygon mesh , computer science , mathematical analysis , engineering , geometry , boundary value problem , statistics , geodesy , structural engineering , geography
SUMMARY A goal‐oriented algorithm is developed and applied for hp ‐adaptive approximations given by the discontinuous Galerkin finite element method for the biharmonic equation. The methodology is based on the dual problem associated with the target functional. We consider three error estimators and analyse their properties as basic tools for the design of the hp ‐adaptive algorithm. To improve adaptation, the combination of two different error estimators is used, each one at its best efficiency, to guide the tasks of where and how to adapt the approximation spaces. The performance of the resulting hp ‐adaptive schemes is illustrated by numerical experiments for two benchmark problems. Copyright © 2013 John Wiley & Sons, Ltd.