A priori error analysis of the local discontinuous Galerkin method for the viscous Burgers-Poisson system - Nattapol Ploymaklam (2018)
© 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(h k+1 ), when polynomials of degree k ≥ 1 are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.