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 L 2 -stability and error estimate for L 2 -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.

中文翻译：

---

时变双曲方程的一种新的 WENO 弱 Galerkin 有限元方法

摘要 在本文中，我们开发了一种新的 WENO 弱伽辽金有限元方案，用于求解瞬态双曲方程。强加逆风型稳定器以加强方案中的通量方向。对于线性对流方程，我们分析了 L 2 -范数的 L 2 -稳定性和误差估计。我们还研究了使用加权基本非振荡 (WENO) 方法的简单限制器，以获得稳健的程序，以实现高阶精度并捕获尖锐的非振荡冲击转变。该方法适用于线性对流方程和 Burgers 方程。最后，给出了数值例子来验证理论结论。