The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case
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DOI：
10.1090/s0025-5718-1990-1010597-0
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发表时间：
1990-05
影响因子：
2
通讯作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
在本文中，我们研究龙格 - 库塔局部投影间断伽辽金（RKDG）方法的二维形式，该方法在一维情形下已被定义和分析。这些格式是在一般的三角剖分上定义的。它们能够轻松处理边界条件，满足最大值原理，并且在形式上具有一致的高阶精度。文中展示了初步的数值结果，这些结果体现了该格式在各种初边值问题上的性能。
In this paper we study the two-dimensional version of the Runge- Kutta Local Projection Discontinuous Galerkin (RKDG) methods, already de- fined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Prelimi- nary numerical results showing the performance of the schemes on a variety of initial-boundary value problems are shown.