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

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.