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Analysis of a class of nonconforming finite elements for crystalline microstructures |
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| Authors: | Petr Kloucek Bo Li Mitchell Luskin. |
| Affiliation: | 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ; 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ; 206 Church St. SE, School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 |
| 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. |
| Keywords: | Nonconforming finite element error estimate superconvergence numerical quadrature |
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