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Adaptive selection of polynomial degrees on a finite element mesh
Author(s) -
Bertóti E.,
Szabó B.
Publication year - 1998
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/(sici)1097-0207(19980615)42:3<561::aid-nme379>3.0.co;2-7
Subject(s) - estimator , finite element method , mathematics , a priori and a posteriori , polynomial , mathematical optimization , displacement (psychology) , distribution (mathematics) , algorithm , mathematical analysis , statistics , psychology , philosophy , physics , epistemology , psychotherapist , thermodynamics
The problem of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed. An a posteriori error estimator based on the minimum complementary energy principle is proposed which utilizes the displacement vector field computed from the finite element solution. This estimator, designed for p ‐ and hp ‐extensions, is conceptually different from estimators based on residuals or patch recovery which are designed for h ‐extension procedures. The quality of the error estimator is demonstrated by examples. The results show that the effectivity index is reasonably close to unity and the sequences of p ‐distributions obtained with the error indicators closely follow the optimal trajectory. © 1998 John Wiley & Sons, Ltd.