Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential-Reference-Cited by-同舟云学术

Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential

Published:2011-06-29 Issue:3 Volume:119 Page:409-435
ISSN:0029-599X
Container-title:Numerische Mathematik
language:en
Short-container-title:Numer. Math.

Author:

Bartels Sören,Müller Rüdiger

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s00211-011-0389-9.pdf

Reference31 articles.

1. Alikakos N., Bates P., Chen X.: Convergence of the Cahn–Hilliard equation to the Hele-Shaw model. Arch. Rat. Mech. Anal. 128, 165–205 (1994)

2. Allen S., Cahn J. W.: A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta. Metall. 27, 1084–1095 (1979)

3. Bartels S.: A posteriori error analysis for time-dependent Ginzburg–Landau type equations. Numer. Math. 99(4), 557–583 (2005)

4. Bartels, S.: A lower bound for the spectrum of the linearized Allen–Cahn operator near a singularity. Preprint available at http://www.bartels.ins.uni-bonn.de (2010)

5. Barrett J.W., Blowey J.F.: An error bound for the finite element approximation of the Cahn–Hilliard equation with logarithmic free energy. Numer. Math. 72(1), 1–20 (1995)

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