Volume 12, Issue 1
A New Triangular Spectral Element Method II: Mixed Formulation and $hp$-Error Estimates

Bingzhen Zhou, Bo Wang, Li-Lian Wang & Ziqing Xie

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 72-97.

Published online: 2018-09

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  • Abstract

Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper. The method is based on equivalent first order system of the elliptic problem and  rectangle-triangle transforms. It fully enjoys the tensorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh. Different from the usual Galerkin formulation, the mixed form is particularly advantageous in this context, since it can avoid the singularity induced by the rectangle-triangle transform in the calculation of the matrices, and does not require the evaluation of the stiffness matrix. An $hp$ a priori error estimate is presented for the proposed method. The implementation details and some numerical examples are provided to validate the accuracy and flexibility of the method.

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@Article{NMTMA-12-72, author = {}, title = {A New Triangular Spectral Element Method II: Mixed Formulation and $hp$-Error Estimates}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {1}, pages = {72--97}, abstract = {

Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper. The method is based on equivalent first order system of the elliptic problem and  rectangle-triangle transforms. It fully enjoys the tensorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh. Different from the usual Galerkin formulation, the mixed form is particularly advantageous in this context, since it can avoid the singularity induced by the rectangle-triangle transform in the calculation of the matrices, and does not require the evaluation of the stiffness matrix. An $hp$ a priori error estimate is presented for the proposed method. The implementation details and some numerical examples are provided to validate the accuracy and flexibility of the method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0038}, url = {http://global-sci.org/intro/article_detail/nmtma/12691.html} }
TY - JOUR T1 - A New Triangular Spectral Element Method II: Mixed Formulation and $hp$-Error Estimates JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 72 EP - 97 PY - 2018 DA - 2018/09 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0038 UR - https://global-sci.org/intro/article_detail/nmtma/12691.html KW - AB -

Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper. The method is based on equivalent first order system of the elliptic problem and  rectangle-triangle transforms. It fully enjoys the tensorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh. Different from the usual Galerkin formulation, the mixed form is particularly advantageous in this context, since it can avoid the singularity induced by the rectangle-triangle transform in the calculation of the matrices, and does not require the evaluation of the stiffness matrix. An $hp$ a priori error estimate is presented for the proposed method. The implementation details and some numerical examples are provided to validate the accuracy and flexibility of the method.

Bingzhen Zhou, Bo Wang, Li-Lian Wang & Ziqing Xie. (2020). A New Triangular Spectral Element Method II: Mixed Formulation and $hp$-Error Estimates. Numerical Mathematics: Theory, Methods and Applications. 12 (1). 72-97. doi:10.4208/nmtma.OA-2018-0038
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