论文标题
对称双曲系统的弱伽勒金有限元法
The Weak Galerkin Finite Element Method for the Symmetric Hyperbolic Systems
论文作者
论文摘要
在本文中，我们介绍并分析了一种弱绿素有限元（WG）方法，用于求解对称双曲系统。通过允许在元素及其边界上使用不连续的有限元元素彼此独立地使用不连续的有限元素，该方法是高度灵活的。通过引入特殊的弱衍生物，我们构建了稳定的弱彩色方案，并得出了$ o的最佳$ l_2 $ - eRROR估计值（h^{k+\ frac {1} {2}}} $ - 当$ k $ - 订单prolonomials用于$ k $ k \ geq geq 0 $时，用于离散解决方案的订购。作为应用程序，我们讨论了解决求解奇异扰动的对流扩散反应方程的WG方法，并得出了$ \ varepsilon $ - 均匀的误差估计$ k+1/2 $。提供了数值示例以显示提出的WG方法的有效性。
In this paper, we present and analyze a weak Galerkin finite element (WG) method for solving the symmetric hyperbolic systems. This method is highly flexible by allowing the use of discontinuous finite elements on element and its boundary independently of each other. By introducing special weak derivative, we construct a stable weak Galerkin scheme and derive the optimal $L_2$-error estimate of $O(h^{k+\frac{1}{2}})$-order for the discrete solution when the $k$-order polynomials are used for $k\geq 0$. As application, we discuss this WG method for solving the singularly perturbed convection-diffusion-reaction equation and derive an $\varepsilon$-uniform error estimate of order $k+1/2$. Numerical examples are provided to show the effectiveness of the proposed WG method.
