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Volume 15, Issue 1-2
Spectral Element Methods on Hybrid Triangular and Quadrilateral Meshes

Jingliang Li, Heping Ma, Li-Lian Wang & Hua Wu

Int. J. Numer. Anal. Mod., 15 (2018), pp. 111-133.

Published online: 2018-01

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  • Abstract

In this paper, we implement and analyse a spectral element method (SEM) on hybrid triangular and quadrilateral element meshes, where the elemental transformation between the triangular element and the reference element is based on the mapping in [17]. We introduce the notion of "quasi-interpolation" to glue the hybrid elements which can build in the singularity of the elemental mapping, and only affects one coefficient of the tensorial nodal basis expansion. Therefore, the hybrid method can be implemented as efficiently as the usual quadrilateral SEM. We also rigorously analyse the "quasi-interpolation" error and the convergence of the hybrid SEM, which show the spectral accuracy can be kept.

  • Keywords

Triangule-rectangle mapping, spectral element method, polygon domain.

  • AMS Subject Headings

65N35, 41A25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fxljl@just.edu.cn (Jingliang Li)

hpma@shu.edu.cn (Heping Ma)

LiLian@ntu.edu.sg (Li-Lian Wang)

hwu@staff.shu.edu.cn (Hua Wu)

  • BibTex
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  • TXT
@Article{IJNAM-15-111, author = {Li , JingliangMa , HepingWang , Li-Lian and Wu , Hua}, title = {Spectral Element Methods on Hybrid Triangular and Quadrilateral Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {111--133}, abstract = {

In this paper, we implement and analyse a spectral element method (SEM) on hybrid triangular and quadrilateral element meshes, where the elemental transformation between the triangular element and the reference element is based on the mapping in [17]. We introduce the notion of "quasi-interpolation" to glue the hybrid elements which can build in the singularity of the elemental mapping, and only affects one coefficient of the tensorial nodal basis expansion. Therefore, the hybrid method can be implemented as efficiently as the usual quadrilateral SEM. We also rigorously analyse the "quasi-interpolation" error and the convergence of the hybrid SEM, which show the spectral accuracy can be kept.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10559.html} }
TY - JOUR T1 - Spectral Element Methods on Hybrid Triangular and Quadrilateral Meshes AU - Li , Jingliang AU - Ma , Heping AU - Wang , Li-Lian AU - Wu , Hua JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 111 EP - 133 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10559.html KW - Triangule-rectangle mapping, spectral element method, polygon domain. AB -

In this paper, we implement and analyse a spectral element method (SEM) on hybrid triangular and quadrilateral element meshes, where the elemental transformation between the triangular element and the reference element is based on the mapping in [17]. We introduce the notion of "quasi-interpolation" to glue the hybrid elements which can build in the singularity of the elemental mapping, and only affects one coefficient of the tensorial nodal basis expansion. Therefore, the hybrid method can be implemented as efficiently as the usual quadrilateral SEM. We also rigorously analyse the "quasi-interpolation" error and the convergence of the hybrid SEM, which show the spectral accuracy can be kept.

Li , JingliangMa , HepingWang , Li-Lian and Wu , Hua. (2018). Spectral Element Methods on Hybrid Triangular and Quadrilateral Meshes. International Journal of Numerical Analysis and Modeling. 15 (1-2). 111-133. doi:
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