Abstract—This paper deals with a high-order accurate Nodal Discontinuous Galerkin (DG) method for the numerical solution of the inviscid Burgers equation, which is a simplest case of nonlinear, hyperbolic partial differential equation. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within elements. In Nodal DG method a finite element space discretization is obtained by element wise discontinuous approximations. Whereas low-storage, high order accurate, explicit Runge-Kutta (LSERK) method is used for temporal discretization. The resulting RKDG methods are stable, high-order accurate and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. Exponential filter is used to remove spurious oscillations near the shock waves. The and errorsin the solution show that the scheme is accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the hyperbolic partial differential equations.

Index Terms—Nodal Discontinuous galerkin method, burgers equation, exponential filter, hyperbolic PDE.

Authors are with the Northwestern Polytechnical University, Xi’ an, China (Tel.: +8618629067124; e-mail: address:fareedmuet@yahoo.com).

Cite: Fareed Ahmed, Faheem Ahmed,Yonghang Guo, and Yong Yang, "A High Order Accurate Nodal Discontinuous Galerkin Method (DGM) for Numerical Solution of Hyperbolic Equation," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 362-364, 2012.