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MATHEMATICS OF COMPUTATION Volume 00, Number 0, Xxxx XXXX, Pages 000 000
 

Summary: MATHEMATICS OF COMPUTATION
Volume 00, Number 0, Xxxx XXXX, Pages 000 000
S 0025-5718XX0000-0
In Math. Comp., 67 : 1998, 917 946.
NONCONFORMING FINITE ELEMENT APPROXIMATION OF
CRYSTALLINE MICROSTRUCTURE
BO LI AND MITCHELL LUSKIN
Abstract. We consider a class of nonconforming nite element approxima-
tions of a simply laminated microstructure which minimizes the nonconvex
variational problem for the deformation of martensitic crystals which can un-
dergo either an orthorhombic to monoclinic double well or a cubic to tetrag-
onal triple well transformation. We rst establish a series of error bounds
in terms of elastic energies for the L2 approximation of derivatives of the de-
formation in the direction tangential to parallel layers of the laminate, for the
L2 approximation of the deformation, for the weak approximation of the de-
formation gradient, for the approximation of volume fractions of deformation
gradients, and for the approximation of nonlinear integrals of the deformation
gradient. We then use these bounds to give corresponding convergence rates
for quasi-optimal nite element approximations.
1. Introduction

  

Source: Akabas, Myles - Department of Physiology and Biophysics, Albert Einstein College of Medicine, Yeshiva University
Luskin, Mitchell - School of Mathematics, University of Minnesota

 

Collections: Biology and Medicine; Materials Science