Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation

Solving the wave equation by a C o finite element method requires to mass-lump the term in time of the variational f6rmulation in order to avoid the inversion of a n-diagonal symmetric matrix at each time-step of the algorithm. One can easily get this mass-lumping on quadrilateral meshes by using a h-version of the spectral elements, based on Gauss-Lobatto quadrature formulae but the equivalent method is not obvious for triangular meshes. In this paper we construct and analyze new families of triangular finite elements which fulfill the same requirements as spectral quadratic and cubic finite elements.