A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy

Ľubomír Baňas; Robert Nürnberg

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 5, page 1003-1026
  • ISSN: 0764-583X

Abstract

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We derive a posteriori estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.

How to cite

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Baňas, Ľubomír, and Nürnberg, Robert. "A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 1003-1026. <http://eudml.org/doc/250578>.

@article{Baňas2009,
abstract = { We derive a posteriori estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm. },
author = {Baňas, Ľubomír, Nürnberg, Robert},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Cahn–Hilliard equation; obstacle free energy; linear finite elements; a posteriori estimates; adaptive numerical methods; Cahn-Hilliard equation; linear finite elements; a posteriori error estimates; elliptic variational equality and inequality; backward Euler discretization; robustness; numerical experiments},
language = {eng},
month = {6},
number = {5},
pages = {1003-1026},
publisher = {EDP Sciences},
title = {A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy},
url = {http://eudml.org/doc/250578},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Baňas, Ľubomír
AU - Nürnberg, Robert
TI - A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/6//
PB - EDP Sciences
VL - 43
IS - 5
SP - 1003
EP - 1026
AB - We derive a posteriori estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.
LA - eng
KW - Cahn–Hilliard equation; obstacle free energy; linear finite elements; a posteriori estimates; adaptive numerical methods; Cahn-Hilliard equation; linear finite elements; a posteriori error estimates; elliptic variational equality and inequality; backward Euler discretization; robustness; numerical experiments
UR - http://eudml.org/doc/250578
ER -

References

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