Local Discontinuous Galerkin Finite Element Method For Two- Dimensional Sobolev Equation

In this paper, we present a scheme based on the local discontinuous Galerkin method for two-dimensional Sobolev Equation. Its L2 norm stability and error estimate are also given. The semidiscrete scheme is proved to have an optimal error estimate of order O(hk+1) when upwind numerical fluxes are used, where h is the maximal mesh parameter and k is the highest degree of each variable in tensor product polynomial-s. The LDG scheme has flexibility in the way of time marching and convenience in software implementation. Finally a numerical result is given to verify our analysis.