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Creators/Authors contains: "Glowinski, Roland"

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  1. ; ; ; (, ESAIM: Control, Optimisation and Calculus of Variations)
    Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinsk, R.; Leugering, G.; Trélat, E.; Zhang, X. (Ed.)
    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. 
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