{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

Brenner, Susanne C and Gudi, Thirupathi and Neilan, Michael and Sung, Li-Yeng (2011) {C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation. In: Mathematics of Computation, 80 (276). pp. 1979-1995.

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Abstract

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

Item Type:	Journal Article
Publication:	Mathematics of Computation
Publisher:	American Mathematical Society
Additional Information:	Copyright of this article belongs to American Mathematical Society.
Keywords:	Monge-Ampere equation;fully nonlinear PDEs;finite element method;convergence analysis
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	25 Oct 2011 10:11
Last Modified:	03 Nov 2011 11:08
URI:	http://eprints.iisc.ac.in/id/eprint/41405

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