4 research outputs found
A New Triangular Spectral Element Method I: Implementation and Analysis on a Triangle
This paper serves as our first effort to develop a new triangular spectral
element method (TSEM) on unstructured meshes, using the rectangle-triangle
mapping proposed in the conference note [21]. Here, we provide some new
insights into the originality and distinctive features of the mapping, and show
that this transform only induces a logarithmic singularity, which allows us to
devise a fast, stable and accurate numerical algorithm for its removal.
Consequently, any triangular element can be treated as efficiently as a
quadrilateral element, which affords a great flexibility in handling complex
computational domains. Benefited from the fact that the image of the mapping
includes the polynomial space as a subset, we are able to obtain optimal -
and -estimates of approximation by the proposed basis functions on
triangle. The implementation details and some numerical examples are provided
to validate the efficiency and accuracy of the proposed method. All these will
pave the way for developing an unstructured TSEM based on, e.g., the
hybridizable discontinuous Galerkin formulation