MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION

Abstract

Solving the acoustics equation by finite elements with mass-lumping requires the use of spectral elements. Although avoiding the inversion of a mass-matrix 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 classical spectral elements and this method, we give a dispersion analysis on nonregular periodic meshes. Then, we analyze the accuracy and the stability of Q3 and Q5 approximations on numerical tests in 2D.