TY - JFULL AU - Faheem Ahmed and Fareed Ahmed and Yongheng Guo and Yong Yang PY - 2012/9/ TI - High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation T2 - International Journal of Physical and Mathematical Sciences SP - 1065 EP - 1071 VL - 6 SN - 1307-6892 UR - https://publications.waset.org/pdf/14926 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 68, 2012 N2 - This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. 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 the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations. ER -