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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Discrete compactness and the approximation of Maxwell’s equations in $\mathbb {R}^3$
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by P. Monk and L. Demkowicz PDF
Math. Comp. 70 (2001), 507-523 Request permission

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 $h$-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.
References
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Additional Information
  • P. Monk
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Newark DE 19716, USA
  • MR Author ID: 126400
  • Email: monk@math.udel.edu
  • L. Demkowicz
  • Affiliation: TICAM, University of Texas at Austin, Austin TX 78712, USA
  • Email: leszek@brahma.ticam.utexas.edu
  • Received by editor(s): October 27, 1998
  • Received by editor(s) in revised form: April 1, 1999
  • Published electronically: February 23, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 507-523
  • MSC (2000): Primary 65N30; Secondary 65N15, 65N25
  • DOI: https://doi.org/10.1090/S0025-5718-00-01229-1
  • MathSciNet review: 1709155