A stabilized discontinuous galerkin method for the nonlinear advection-diffusion processes

This article presents a hybridization of a local discontinu- ous Galerkin method (LDG) with the Ø method to capture nonlinear behavior of the advection-diffusion processes. The predetermined fixed ux selection is extended to the generalized problem-dependent ux se- lection in the LDG algorithm. The derived technique has been shown to be unconditionally stable through the L2 stability analysis. Two il- lustrative test problems are considered to demonstrate the effciency of the currently produced technique for both advection and diffiusion dom- inated processes.