Discontinuous Galerkin method for the fully dynamic Biot's model

In this paper, a fully discrete scheme of the fully dynamic Biot's model problem is proposed, which is constructed by using interior penalty discontinuous Galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms. First of all, we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms. Then, based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure. Finally, a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic Biot's model problem. (C) 2020 Elsevier Inc. All rights reserved.