NURBS‐enhanced finite element method (NEFEM)

descriptionPublicationkeyboard_double_arrow_right Article 19 Feb 2008 English Publisher:WileyJournal:International Journal for Numerical Methods in Engineering, volume 76, pages 56-83 (issn: 0029-5981, eissn: 1097-0207,

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Authors: Sevilla Cárdenas, Rubén; Fernández Méndez, Sonia; Huerta, Antonio;

doi: 10.1002/nme.2311

handle: 2117/16600 , 2117/8158

NURBS‐enhanced finite element method (NEFEM)

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Abstract

AbstractAn improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non‐uniform rational B‐splines (NURBS). Here, the 2D case is presented. For elements not intersecting the boundary, a standard FE interpolation and numerical integration are used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NURBS‐enhanced finite element method (NEFEM) is at least one order of magnitude more precise than the corresponding isoparametric FE in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision, NEFEM is also more computationally efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing an accurate solution with coarse meshes and high‐order interpolations makes NEFEM a more efficient strategy than classical isoparametric FE. Copyright © 2008 John Wiley & Sons, Ltd.

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Swansea University
United Kingdom

Keywords

Elements finits, a priori error estimates, Engineering, Civil, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits, Engineering, Multidisciplinary, :Matemàtiques i estadística::Geometria::Geometria algebraica [Àrees temàtiques de la UPC], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Poisson equation, :Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits [Àrees temàtiques de la UPC], computer-aided design, Algebraic, Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory, Elements finits, Mètode dels -- Anàlisi numèrica, Engineering, Ocean, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Engineering, Aerospace, Engineering, Biomedical, Curves, Mètode dels -- Anàlisi numèrica, numerical examples, airfoil equation, Spline theory, Computer Science, Software Engineering, 65D Numerical approximation and computational geometry, Curves, Algebraic, Engineering, Marine, high-order isoparametric finite elements, Engineering, Manufacturing, Engineering, Mechanical, electromagnetic scattering, exact geometry representation, Splines (Matemàtica), Engineering, Industrial, finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Corbes algebraiques, transient Maxwell equations, non-uniform rational B-splines (NURBS), Diffraction, scattering, Finite element methods applied to problems in fluid mechanics, discontinuous Galerkin, Numerical analysis

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