A weak Galerkin finite element method for solving nonlinear convection-diffusion problems in two dimensions

摘要

We study weak Galerkin (WG) finite element method (FEM) for solving nonlinear convection-diffusion problems. A WG finite element scheme is presented based on a new variational form. We prove the energy conservation law and stability of the continuous time WG FEM. In particular, optimal order error estimates are established for the WG FEM approximation in both a discrete H1-norm and L2-norm. Numerical experiments are performed to confirm the theoretical results.