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Comparison of high‐order curved finite elements
Author(s) -
Sevilla Ruben,
FernándezMéndez Sonia,
Huerta Antonio
Publication year - 2011
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.3129
Subject(s) - finite element method , discretization , mathematics , computation , discontinuous galerkin method , representation (politics) , cartesian coordinate system , consistency (knowledge bases) , boundary (topology) , mixed finite element method , extended finite element method , galerkin method , mathematical analysis , smoothed finite element method , boundary value problem , boundary knot method , geometry , algorithm , boundary element method , structural engineering , engineering , politics , political science , law
Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two‐dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS‐enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p ‐FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations. Copyright © 2011 John Wiley & Sons, Ltd.