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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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.
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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