The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

Download or read book The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-13 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown. Cockburn, Bernardo and Shu, Chi-Wang Langley Research Center NAS1-19480; DAAH04-94-G-0205; NSF DMS-94-00814; NSF DMS-94-07952; NAG1-1145; AF-AFOSR-95-1-0074; RTOP 505-90-52-01...