Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation

摘要

This paper proposes a discontinuous Galerkin method to solve the generalized Sobolev equation. In this numerical procedure, the temporal variable has been discretized by the Crank-Nicolson idea to get a time-discrete scheme with the second-order accuracy. Then, in the second stage the spatial variable has been discretized by the discontinuous Galerkin finite element method. A prior error estimate has been proposed for the semi-discrete scheme based on the spatial discretization. By applying the Crank-Nicolson idea a full-discrete scheme is driven. Furthermore, an error estimate has been proved to get the convergence order of the developed scheme. Finally, some numerical examples have been presented to show the efficiency and theoretical results of the new numerical procedure.