A Priori Error Analysis of the Local Discontinuous Galerkin Method for the Viscous Burgers-Poisson System

Abstract

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 $\mathcal{O}(h^{k+1})$, when polynomials of degree $k\geq 1$ are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.