Abstract
In this paper, we develop a new WENO weak Galerkin finite element scheme for solving the time dependent hyperbolic equations. The upwind-type stabilizer is imposed to enforce the flux direction in the scheme. For the linear convection equations, we analyze the L2-stability and error estimate for L2-norm. We also investigate a simple limiter using weighted essentially non-oscillatory (WENO) methodology for obtaining a robust procedure to achieve high order accuracy and capture the sharp, non-oscillatory shock transitions. The approach applies for linear convection equations and Burgers equations. Finally, numerical examples are presented for validating the theoretical conclusions.
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