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A hybridizable discontinuous triangular spectral element method on unstructured meshes and its hp-error estimates

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Abstract

In this paper, a hybridizable discontinuous triangular spectral element method (HDTSEM) using tensorial nodal basis functions on unstructured meshes is proposed and analyzed. The elemental local basis is constructed from the one-to-one rectangle-to-triangle transform (Li et al., Lecture Notes in Computational Sciences and Engineering 76:237–246, 2011) and glued together under the hybridizable discontinuous Galerkin (HDG) framework. This offers much flexibility allowing for mismatch in nodal points across elements, substantial reduction in global degree of freedoms (DoFs) and excellent mesh adaptivity without sacrificing the high accuracy of a typical spectral element method (SEM). Here, optimal L2-error estimates are obtained on quasi-uniform unstructured meshes and ample numerical results are provided to validate the theoretical results.

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Acknowledgements

The first and second authors received financial support provided by NSFC (grant 11771137, 12022104) and the Construct Program of the Key Discipline in Hunan Province. The research of the first author is partially supported by Hunan Provincial Innovation Foundation for Postgraduate (grant CX20190337). The research of the third author is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 Grants (MOE2018-T2-1-059 and MOE2017-T2-2-144). The fourth author is partially supported by NSFC (11771138).

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Authors and Affiliations

  1. Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Bingzhen Zhou, Bo Wang & Ziqing Xie

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Li-Lian Wang

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  1. Bingzhen Zhou
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  2. Bo Wang
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  3. Li-Lian Wang
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  4. Ziqing Xie
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Correspondence to Bo Wang.

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Zhou, B., Wang, B., Wang, LL. et al. A hybridizable discontinuous triangular spectral element method on unstructured meshes and its hp-error estimates. Numer Algor 91, 1231–1260 (2022). https://doi.org/10.1007/s11075-022-01300-3

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  • DOI: https://doi.org/10.1007/s11075-022-01300-3

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