Mortar Triangular Spectral Element Method

This paper presents a Mortar triangular spectral element method with spectral accuracy on unstructured grid.Based on the mapping from quadrangle to triangle,this method constructs the node basis functions of triangular spectral elements in the form of tensor product and the corresponding triangular spectral element space.This Mortar technology successfully solved the node mismatch on the common edge of adjacent units due to the mapping from quadrangle to triangle.By changing the second order elliptic problem into a first order form and then discretizing it into a mixed form,the integral singularity problem in stiffness matrix calculation is avoided.In this paper,the approximation properties of Mortar spectral element space were analyzed,the implementation of the algorithm was introduced in detail,and a large number of numerical examples were given for the elliptic problem.The results show that the new method achieves the optimal convergence order with respect to the grid step size ? and polynomial degreep.