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The performance of Bank‐Weiser's error estimator for quadrilateral finite elements
Author(s) -
Ainsworth Mark
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100508
Subject(s) - quadrilateral , mathematics , estimator , counterexample , norm (philosophy) , polygon mesh , finite element method , degree (music) , pure mathematics , mathematical analysis , discrete mathematics , geometry , statistics , physics , political science , acoustics , law , thermodynamics
The error estimator proposed by Bank and Weiser is analyzed in the case of degree p finite element approximations on quadrilateral meshes. It is shown that the scheme is asymptotically exact in the energy norm for regular solutions provided that the degree of approximation is of odd order and the elements are rectangles . Perhaps surprisingly, the hypotheses are necessary, as counterexamples show. © 1994 John Wiley & Sons, Inc.