A Local Discontinuous Galerkin Method for the Reduced Burgers-Poisson Equation

Nattapol Ploymaklam

Abstract

In this work, we discuss a numerical approximation of the solution of the reduced Burgers-Poisson equation using the local discontinuous Galerkin method (LDG). The reduced Burgers-Poisson equation comes from rewriting the system of Burger-Poisson equations into a single equation. The equation is then rewritten into a system of first-order partial differential equation before the discontinuous Galerkin framework is applied.   Numerical tests show that optimal order of convergence can be achieved when using polynomials of even degree in the approximation. The result agrees with the behavior of the numerical solution of the system of Burgers-Poisson equations using LDG.