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Finite element approximations of the three dimensional Monge-Ampère equation

Published online by Cambridge University Press:  13 February 2012

Susanne Cecelia Brenner
Affiliation:
Department of Mathematics and Center for Computation & Technology, Louisiana State University, Baton Rouge, 70803 LA, USA. brenner@math.lsu.edu ; Supported in part by the National Science Foundation under Grant Numbers DMS-07-13835 and DMS-10-16332. ,
Michael Neilan
Affiliation:
Department of Mathematics, University of Pittsburgh, 15260 PA USA; neilan@pitt.edu ,
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2012

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