Mathematics of Computation

Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R} ^3$

Author(s): P. Monk; L. Demkowicz.
Journal: Math. Comp. 70 (2001), 507-523.
MSC (2000): Primary 65N30; Secondary 65N15, 65N25
Posted: February 23, 2000
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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.

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P. Monk
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark DE 19716, USA
Email: monk@math.udel.edu

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