Comparison of high-order curved finite elements

Author (s): Sevilla, R.; Fernandez-Mendez, S. and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 87, Issue 8
Pages: 719 – 734
Date: 2011

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 in 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 methods (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.



author = {Ruben Sevilla and Sonia Fernández‐Méndez and Antonio Huerta},
title = {Comparison of high‐order curved finite elements},
journal = {International Journal for Numerical Methods in Engineering},
volume = {87},
number = {8},
pages = {719-734},
keywords = {finite element method, isoparametric FEM, Cartesian FEM, p‐version FEM, NURBS‐enhanced FEM, exact geometry},
doi = {10.1002/nme.3129},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.3129},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.3129},
aCopyright © 2011 John Wiley \& Sons, Ltd.}