Construction of Jacobian Matrix for Solving Convection-Diffusion Problem with Interior Penalty Method. Issue 5 (February 2019) - Li, Liang; Wu, Songping
Abstract: In this paper we describe in details constructing the Jacobian matrix based on the interior penalty discontinuous Galerkin discretization of the time-dependent convection-diffusion problem, which is requisite for the nonlinear solver when an implicit method is used in time integration. Special attention is paid to the treatment of periodic boundary conditions during the construction. The convergence rate of the nonlinear solver is tested in numerical simulation to illustrate the utility of the Jacobian matrix.