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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Abstract

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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.

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Brenner, 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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