The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients

Abstract

In this article, we will apply a space-time continuous Galerkin (CG) method to solve the numerical solution of Sobolev equation with space-time variable coefficients. Both the spatial and temporal variables of this method are discretized by finite element (FE) method, and hence it can easily attain the high order precision both in space and time directions as well as have the good stability. In addition, the variable spatial grid structures from one time span to the next and the time steps are permitted for this method, which are more suitable to design adaptive algorithm on unstructured mesh. We detailedly give the well-posed analysis of the numerical solution and the a priori error estimation in L∞(H1) norm without any restrictions on the space-time grid ratio. Finally, some numerical experiments are showed to conform the convergence orders and validate the high efficiency for the method investigated here.