A STABILIZED PRIMAL HYBRID FINITE ELEMENT FORMULATION FOR THE ELASTIC WAVE EQUATION

Resumo

We present a stabilized hybrid finite element formulation for the elastic wave equation in two space
dimensions. The proposed hybrid formulation is characterized by the introduction of auxiliary variables on the
edges of the elements, which are identified as Lagrange multipliers associated with the trace of displacement field.
A second order explicit finite difference method is adopted in the time domain. It is well known that when this
second order ”explicit” finite difference approximation in time is combined with classical Continuous Galerkin
finite element approximations in space it does not lead to a really explicit method, given that the consistent mass
matrix in this case is non diagonal. With the proposed formulation it is possible to obtain really explicit methods
with block-diagonal mass matrices. Even diagonal mass matrices can also be obtained, as long as the Lagrangian

interpolation functions are centered in the Gauss integration points. Convergence studies are conducted on uni-
form and on randomly generated non-uniform quadrilateral meshes. Meshes with straight or curved quadrilateral

elements are considered, associated with Lagrangian bases and with Qk and Pk monomial bases.