The totally volume local discontinuous Galerkin method for viscous Burgers’ equations.

Abstract

In this paper, the totally volume local discontinuous Galerkin TV-LDG method is proposed to solve the viscous Burgers’ equations with appropriate initial and boundary conditions. Time derivative is discretized by the third-order strong stability preserving Runge Kutta explicit SSP-RK (3, 3) method. Space derivatives discretization is performed by the totally volume local discontinuous Galerkin method. Finally, the validity of proposed scheme is demonstrated by numerical experiments and shows that the present scheme offers better accuracy in comparison with other existing numerical methods.