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A New WENO Weak Galerkin Finite Element Method for Time Dependent Hyperbolic Equations
Applied Numerical Mathematics ( IF 2.2 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.apnum.2020.09.002
Lin Mu , Zheng Chen

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。
更新日期:2021-01-01
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