A new upwind weak Galerkin finite element method for linear hyperbolic equations (Q2226316)

To develop a numerical method for the discontinuous solutions to a linear hyperbolic equations without spurious oscillations is still a challenge. Among lots of numerical methods, the discontinuous Galerkin method is a class of effective approaches for such kind of hyperbolic equations, and is extensively investigated. As an alternative approach, the author developed a new upwind weak Galerkin finite element scheme for them in this paper. The upwind-type stabilizer was imposed in the scheme. An error estimate was investigated for a suitable norm. In order to validate the theoretical conclusions, the author also presented numerical examples in the end of the paper.