Volume 9, Issue 4
Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods

S. P. Oliveira & G. Seriani

Commun. Comput. Phys., 9 (2011), pp. 937-958.

Published online: 2011-09

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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.

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@Article{CiCP-9-937, author = {}, title = {Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {4}, pages = {937--958}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.071109.080710a}, url = {http://global-sci.org/intro/article_detail/cicp/7529.html} }
TY - JOUR T1 - Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods JO - Communications in Computational Physics VL - 4 SP - 937 EP - 958 PY - 2011 DA - 2011/09 SN - 9 DO - http://doi.org/10.4208/cicp.071109.080710a UR - https://global-sci.org/intro/article_detail/cicp/7529.html KW - AB -

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.

S. P. Oliveira & G. Seriani. (2020). Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods. Communications in Computational Physics. 9 (4). 937-958. doi:10.4208/cicp.071109.080710a
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