A STABILIZED DISCONTINUOUS GALERKIN METHOD FOR THE NONLINEAR ADVECTION-DIFFUSION PROCESSES

Abstract

This article presents a hybridization of a local discontinuous Galerkin method (LDG) with the theta-method to capture nonlinear behavior of the advection-diffusion processes. The predetermined fixed flux selection is extended to the generalized problem-dependent flux selection in the LDG algorithm. The derived technique has been shown to be unconditionally stable through the L-2 stability analysis. Two illustrative test problems are considered to demonstrate the efficiency of the currently produced technique for both advection and diffusion dominated processes.