Superconvergence results for Galerkin methods for wave propagation in various porous media

Finite-element methods are considered for numerically solving the equations describing wave propagation in various porous media such as inhomogeneous elastic media, fluid saturated media, composite isotropic inhomogeneous elastic media, composite anisotropic media, etc. Quasi-projection analyses based on an asymptotic expansion to high order of finite-element solutions are given to obtain error estimates in Sobolev spaces of nonpositive index for the approximate solution. Superconvergence phenomena for the finite-element methods under consideration are also investigated. © 1996 John Wiley & Sons, Inc.