# 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

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topBaňas, 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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