Journal
NUMERICAL ALGORITHMS
Volume 91, Issue 3, Pages 1231-1260Publisher
SPRINGER
DOI: 10.1007/s11075-022-01300-3
Keywords
Spectral element method; Hybridizable discontinuous Galerkin method; Unstructured triangular mesh; hp error analysis
Categories
Funding
- NSFC [11771137, 12022104, 11771138]
- Construct Program of the Key Discipline in Hunan Province
- Hunan Provincial Innovation Foundation for Postgraduate [CX20190337]
- Ministry of Education, Singapore, under its MOE AcRF Tier 2 Grants [MOE2018-T2-1-059, MOE2017-T2-2-144]
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In this paper, a hybridizable discontinuous triangular spectral element method (HDTSEM) using tensorial nodal basis functions on unstructured meshes is proposed and analyzed. The method allows for mismatch in nodal points across elements, reduces global degrees of freedom, and maintains the high accuracy and mesh adaptivity of a typical spectral element method.
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 L-2-error estimates are obtained on quasi-uniform unstructured meshes and ample numerical results are provided to validate the theoretical results.
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