Discrete compactness and the approximation of Maxwell's equations in R3
Discrete compactness and the approximation of Maxwell's equations in R3
复制标题
DOI：
10.1090/s0025-5718-00-01229-1
复制
发表时间：
2001-04
期刊：
影响因子：
--
通讯作者：
P. Monk;L. Demkowicz
中科院分区：
文献类型：
--
作者：
P. Monk;L. Demkowicz
我们分析了在有界腔体中使用棱边有限元方法来近似麦克斯韦方程。利用集体紧算子理论，我们证明了源问题和特征值问题的h-收敛性。这是一般棱边元特征值问题收敛性的第一个证明，它扩展和统一了这两个问题的理论。收敛性结果是基于菊池的棱边元的离散紧性。我们延长原来的工作菊池证明，所有订单的边缘元素拥有此属性。
We analyze the use of edge finite element methods to approximate Maxwell's equations in a bounded cavity. Using the theory of collectively compact operators, we prove h-convergence for the source and eigenvalue problems. This is the first proof of convergence of the eigenvalue problem for general edge elements, and it extends and unifies the theory for both problems. The convergence results are based on the discrete compactness property of edge element due to Kikuchi. We extend the original work of Kikuchi by proving that edge elements of all orders possess this property.