Volume 46, Number 5, September-October 2012
|Page(s)||979 - 1001|
|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
2 Department of Mathematics, University of Pittsburgh, 15260 PA USA ,
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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