A STABILIZED DISCONTINUOUS GALERKIN METHOD FOR THE NONLINEAR ADVECTION-DIFFUSION PROCESSES - Tunc, Huseyin; Sari, Murat (INST MATHEMATICS & MECHANICS, NATL ACAD SCIENCES AZERBAIJAN, 2021)
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.
Keywords: Advection-diffusion processes; Local discontinuous Galerkin method; Burgers equation; theta-method; Hopf-Cole transformation; Mathematics