| Issue |
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
|
|
|---|---|---|
| Page(s) | 979 - 1001 | |
| DOI | https://doi.org/10.1051/m2an/2011067 | |
| Published online | 13 February 2012 | |
Finite element approximations of the three dimensional Monge-Ampère equation
1 Department of Mathematics and Center
for Computation & Technology, Louisiana State University,
Baton Rouge, 70803
LA,
USA
,
brenner@math.lsu.edu
2 Department of Mathematics, University
of Pittsburgh, 15260
PA
USA
,
neilan@pitt.edu
Received:
19
July
2010
Revised:
19
May
2011
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.
Mathematics Subject Classification: 65N30 / 35J60
Key words: Monge-Ampère equation / three dimensions / finite element method / convergence analysis
© EDP Sciences, SMAI, 2012
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