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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.

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Analysis of a class of nonconforming finite elements for crystalline microstructures
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by Petr Kloucek, Bo Li and Mitchell Luskin PDF
Math. Comp. 65 (1996), 1111-1135 Request permission

Abstract:

An analysis is given for a class of nonconforming Lagrange-type finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed in 1992 by Rannacher and Turek for the Stokes equation. Our analysis highlights the features of these elements which make them effective for the computation of microstructure. New results for superconvergence and numerical quadrature are also given.
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Additional Information
  • Petr Kloucek
  • Affiliation: 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: kloucek@math.umn.edu
  • Bo Li
  • Affiliation: 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: bli@math.umn.edu
  • Mitchell Luskin
  • Affiliation: 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: luskin@math.umn.edu
  • Received by editor(s): March 8, 1994
  • Received by editor(s) in revised form: May 30, 1995
  • Additional Notes: This work was supported in part by the NSF through grant DMS 911-1572, by the AFOSR through grant AFOSR-91-0301, by the ARO through grants DAAL03-89-G-0081 and DAAL03-92-G-0003, and by a grant from the Minnesota Supercomputer Institute.
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 1111-1135
  • MSC (1991): Primary 65N15, 65N30, 35J20, 35J70, 73V25
  • DOI: https://doi.org/10.1090/S0025-5718-96-00735-1
  • MathSciNet review: 1344616