Finite element approximations of the three dimensional Monge-Ampère equation
Susanne Cecelia Brenner, Michael Neilan (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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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. ...