Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14563
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Main Title: Analysis and simulation for an isotropic phase-field model describing grain growth
Author(s): Korzec, Maciek
Wu, Hao
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15790
http://dx.doi.org/10.14279/depositonce-14563
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: A phase-field system of coupled Allen-Cahn type PDEs describing grain growth is analyzed and simulated. In the periodic setting, we prove the existence and uniqueness of global weak solutions to the problem. Then we investigate the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. Namely, the problem possesses a global attractor as well as an exponential attractor, which entails that the global attractor has finite fractal dimension. Moreover, we show that each trajectory converges to a single equilibrium. A time-adaptive numerical scheme based on trigonometric interpolation is presented. It allows to track the approximated long-time behavior accurately and leads to a convergence rate. The scheme exhibits a physically aspired discrete free energy dissipation.
Subject(s): grain growth
phase-field system
well-posedness
long-time behavior
numerical simulation
Issue Date: 11-Mar-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 35K20 Boundary value problems for second-order, parabolic equations
74H40 Long-time behavior of solutions
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 06
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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