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Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods

Published online by Cambridge University Press:  20 August 2015

S.P. Oliveira  and
G. Seriani
S.P. Oliveira*
Affiliation:
Departamento de Matemática, Universidade Federal do Paraná, Curitiba-PR, 81531-980, Brazil
G. Seriani*
Affiliation:
Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Borgo Grotta Gigante, 42/c, Sgonico (TS), 34010, Italy
*
Email:saulopo@ufpr.br
Corresponding author.Email:gseriani@inogs.it
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Abstract

Spectral element methods are well established in the field of wave propagation, in particular because they inherit the flexibility of finite element methods and have low numerical dispersion error. The latter is experimentally acknowledged, but has been theoretically shown only in limited cases, such as Cartesian meshes. It is well known that a finite element mesh can contain distorted elements that generate numerical errors for very large distortions. In the present work, we study the effect of element distortion on the numerical dispersion error and determine the distortion range in which an accurate solution is obtained for a given error tolerance. We also discuss a double-grid calculation of the spectral element matrices that preserves accuracy in deformed geometries.

Keywords

65C2065M6065M7065M1586A1565Z05Spectral element methoddispersion analysisslivering
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 937 - 958
Copyright
Copyright © Global Science Press Limited 2011

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