Mixed finite elements with mass-lumping for the transient wave equation

Solving the acoustics equation by finite elements with mass-lumping require s the use of spectral elements. Although avoiding the inversion of a mass-m atrix at each time-step, these elements remain expensive from the point of view of the stiffness-matrix. In this paper, we give a mixed finite element method which provides a factorization of the stiffness-matrix which leads to a gain of storage and computation time which grows with the order of the method and the dimension in space. After proving the equivalence between c lassical spectral elements and this method, we give a dispersion analysis o n nonregular periodic meshes. Then, we analyze the accuracy and the stabili ty of Q(3) and Q(5) approximations on numerical tests in 2D.