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TESTING OF HIGHER ORDER FINITE ELEMENTS BASED ON LAGRANGE POLYNOMIALS IN DEPENDENCE OF THE UNDERLYING NODAL GRID

Schmicker, D.; Vivar-Perez, J.M.; Gabbert, U.;

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The paper deals with the investigation of a higher order finite element method utilizing Lagrangian interpolation polynomials as shape functions, also often referred to as spectral element method (SEM). The main concern is to analyze the influence of the underlying nodal distribution on the convergence, performance and stability properties of the solution. To this end four different nodal configurations are investigated, namely the equispaced grid (EQ), the Gauss point grid (GP), the Gauss-Lobatto-Legendre grid (GLL) and the Chebyshev-Gauss-Legendre (CGL) grid. It is concluded that the nodal distribution does not alter the convergence behavior directly. Differences are only observed in cases, where, e.g., the approximation of the geometry of distorted elements or the implementation of Dirichlet boundary conditions takes place. It is figured out that the EQ-grid cannot be recommended because of the occurrence of Runge’s oscillations and very high condition numbers, while the other three nodal configurations show an excellent solution quality and behave almost equal. Further tests have revealed that the solution quality of the GLL-element is not significantly affected by the well known mass lumping technique even if the element has a strongly distorted geometry. This makes the GLL-grid favourable in dynamic analyses.

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Palavras-chave: Higher order finite element method, Spectral element method, Convergence studies,

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DOI: 10.5151/meceng-wccm2012-18022

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Como citar:

Schmicker, D.; Vivar-Perez, J.M.; Gabbert, U.; "TESTING OF HIGHER ORDER FINITE ELEMENTS BASED ON LAGRANGE POLYNOMIALS IN DEPENDENCE OF THE UNDERLYING NODAL GRID", p. 541-558 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18022

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