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Title: On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator
In this article, we report the results we obtained when investigating the numerical solution of some nonlinear eigenvalue problems for the Monge-Ampère operator v → det D 2 v . The methodology we employ relies on the following ingredients: (i) a divergence formulation of the eigenvalue problems under consideration. (ii) The time discretization by operator-splitting of an initial value problem (a kind of gradient flow) associated with each eigenvalue problem. (iii) A finite element approximation relying on spaces of continuous piecewise affine functions. To validate the above methodology, we applied it to the solution of problems with known exact solutions: The results we obtained suggest convergence to the exact solution when the space discretization step h → 0. We considered also test problems with no known exact solutions.  more » « less
Award ID(s):
2012046
PAR ID:
10278869
Author(s) / Creator(s):
; ; ;
Editor(s):
Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinsk, R.; Leugering, G.; Trélat, E.; Zhang, X.
Date Published:
Journal Name:
ESAIM: Control, Optimisation and Calculus of Variations
Volume:
26
ISSN:
1292-8119
Page Range / eLocation ID:
118
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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