Hybridization Discontinuous Spectral Element Method On Triangular Mesh

In this paper,the hybrid discontinuous Galerkin methods and spectral el-ement method are combined skillfully,develop a hybrid discontinuous spectral element method on triangular meshes.The method is based on discontinuous triangular spectral element space with the tensor product node basis func-tion constructed by the rectangle to triangle transform,and then the discrete scheme of triangular hybrid discontinuous spectral element is presented under the framework of hybrid discontinuous Galerkin method.The h-p estimation of the interpolation error in the triangular spectral element space is proved.At the same time,the efficient calculation formula for the calculation of the dis-crete matrix is given according to the tensor product form of the basis function.The triangular hybrid discontinuous spectral element not only sharing the ad-vantages of high precision and fast convergence of spectral element method,but also inheriting the advantages of less degrees of freedom and can handle the hang point problem of hybrid discontinuous Galerkin method,more impor-tantly,it's break through the limitation that the gird of the spectral element method must be quadrilateral mesh,and not need to consider the problem of the jacobian singularity in integration caused by the transformation of the rectangle to the triangle.