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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Analysis of a class of nonconforming finite elements for crystalline microstructures


Authors: Petr Kloucek, Bo Li and Mitchell Luskin
Journal: Math. Comp. 65 (1996), 1111-1135
MSC (1991): Primary 65N15, 65N30, 35J20, 35J70, 73V25
MathSciNet review: 1344616
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00735-1
PII: S 0025-5718(96)00735-1
Keywords: Nonconforming finite element, error estimate, superconvergence, numerical quadrature
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.
Article copyright: © Copyright 1996 American Mathematical Society