A priori error analysis of the local discontinuous Galerkin method for the viscous Burgers-Poisson system

Abstract

© 2017 Institute for Scientific Computing and Information. In this paper, we propose and analyze the local discontinuous Galerkin method for the viscous Burgers-Poisson system. The proposed method preserves two invariants and hence, yields solutions even for long time. A priori error estimates, which are of order O(hk+1), when polynomials of degree k ≥ 1 are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.