Discrete compactness and the approximation of Maxwell's equations in ![]() |
| |
Authors: | P. Monk L. Demkowicz. |
| |
Affiliation: | Department of Mathematical Sciences, University of Delaware, Newark DE 19716, USA ; TICAM, University of Texas at Austin, Austin TX 78712, USA |
| |
Abstract: | 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 -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. |
| |
Keywords: | Finite element methods discrete compactness eigenvalues error estimates |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
|
点击此处可从《Mathematics of Computation》下载全文 |