A weak Galerkin finite element method for Burgers' equation

We propose a weak Galerkin (WG) finite element method for solving the one-dimensional Burgers' equation. Based on a new weak variational form, both semi-discrete and fully-discrete WG finite element schemes are established and analyzed. We prove the existence of the discrete solution and derive the optimal order error estimates in a discrete H1 norm and the standard L2 norm, respectively. Numerical experiments are presented to illustrate our theoretical analysis.