 
Summary: MATHEMATICS OF COMPUTATION
Volume 00, Number 0, Xxxx XXXX, Pages 000 000
S 00255718XX00000
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 quasioptimal nite element approximations.
1. Introduction
