A splitting mixed space-time discontinuous Galerkin method for parabolic problems

摘要

A splitting mixed space-time discontinuous Galerkin method is formulated to solve a class of parabolic problems. This method, in which the stress equation is separated from displacement equation, is based on mixed method and space-time discontinuous finite element method which is discontinuous in time and continuous in space. By a splitting technique, the stress equation is separated from the stress-displacement coupled system. The finite element approximation of the stress is solved by time discontinuous Galerkin method with high accuracy. Then, if required, the discrete displacement function is also solved by the time discontinuous Galerkin method. The convergence of the scheme is analyzed by the technique of combining finite difference and finite element methods. The optimal priori error estimates in L~(∞)(L~2) norm for displacement and in L~(∞)(L~2) norm and L~2 (H(div)) norm for stress are derived, respectively. Numerical experiments are presented to confirm theoretical results.