# Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner; Michael Neilan

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 5, page 979-1001
- ISSN: 0764-583X

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topBrenner, Susanne Cecelia, and Neilan, Michael. "Finite element approximations of the three dimensional Monge-Ampère equation." ESAIM: Mathematical Modelling and Numerical Analysis 46.5 (2012): 979-1001. <http://eudml.org/doc/276379>.

@article{Brenner2012,

abstract = {In this paper, we construct and analyze finite element methods for the three dimensional
Monge-Ampère equation. We derive methods using the Lagrange finite element space such that
the resulting discrete linearizations are symmetric and stable. With this in hand, we then
prove the well-posedness of the method, as well as derive quasi-optimal error estimates.
We also present some numerical experiments that back up the theoretical findings.},

author = {Brenner, Susanne Cecelia, Neilan, Michael},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Monge-Ampère equation; three dimensions; finite element method; convergence analysis; finite element; Lagrange finite element space; well-posedness; numerical results},

language = {eng},

month = {2},

number = {5},

pages = {979-1001},

publisher = {EDP Sciences},

title = {Finite element approximations of the three dimensional Monge-Ampère equation},

url = {http://eudml.org/doc/276379},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Brenner, Susanne Cecelia

AU - Neilan, Michael

TI - Finite element approximations of the three dimensional Monge-Ampère equation

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/2//

PB - EDP Sciences

VL - 46

IS - 5

SP - 979

EP - 1001

AB - In this paper, we construct and analyze finite element methods for the three dimensional
Monge-Ampère equation. We derive methods using the Lagrange finite element space such that
the resulting discrete linearizations are symmetric and stable. With this in hand, we then
prove the well-posedness of the method, as well as derive quasi-optimal error estimates.
We also present some numerical experiments that back up the theoretical findings.

LA - eng

KW - Monge-Ampère equation; three dimensions; finite element method; convergence analysis; finite element; Lagrange finite element space; well-posedness; numerical results

UR - http://eudml.org/doc/276379

ER -

## References

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