Comparison of high-order curved finite elements

Authors

  • Ruben Sevilla,

    Corresponding author
    1. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain
    • Laboratori de Càlcul Numèric (LaCàN), E.T.S. Ingenieros de Caminos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain
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  • Sonia Fernández-Méndez,

    1. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain
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  • Antonio Huerta

    1. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain
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Abstract

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.

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