A weak Galerkin finite element method for Burgers' equation

Abstract

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 the discrete $H^1$-norm and $L^2$-norm, respectively. Numerical experiments are presented to illustrate our theoretical analysis.

25 pages, 5 figures

References in corpus (2)

• A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations
• A weak finite element method for elliptic problems in one space dimension