Spectral Element Methods on Hybrid Triangular and Quadrilateral Meshes

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.