# A $P^1-P^0$ finite element method for a model of polymer
crystallization

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Comput. Methods Appl. Mech.
Engrg., 125 (1995), 303-317.
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Xun Jiang

Department of Mathematics

University of California at Davis

Davis, CA 95616, USA

xun@galois.ucdavis.edu
Ricardo H. Nochetto

Department of Mathematics

University of Maryland, College Park

College Park, MD 20742, USA

rhn@math.umd.edu
Claudio Verdi

Dipartimento di Matematica

Universita di Milano

Milano, 20133, Italy

verdi@paola.mat.unimi.it
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Abstract

We consider a practical finite element approximation of a 3D model for
the crystallization of polymers. The model is a system consisting of
a parabolic PDE for the thermal
balance coupled with several nonlinear ODEs for the crystallization
kinetics. The
isokinetic assumption implies a non-Lipschitz continuous dependence of
the kinetic equations on the crystalline volume fraction.
Piecewise linear elements are used for temperature and piecewise
constants for the kinetic variables.
The numerical algorithm is simple, easy to implement
on a computer, and a linear system with the same symmetric positive definite
matrix has to be solved per time step.
We prove optimal linear $L^\infty L^1$
a priori error estimates in terms of both discretization parameters,
using monotonicity and $L^1$ techniques.
A relevant simulation in 3D with axial symmetry shows qualitative
agreement of the mathematical model with experimental results.