An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic monge-ampere equation in two dimensions.

Electronic Transactions on Numerical Analysis | January 1, 2006| | Copyright

Abstract. In this article, we discuss the numerical solution of the Dirichlet problem for the real elliptic Monge-Ampere equation, in two dimensions, by an augmented Lagrangian based iterative method. To derive the above algorithm, we take advantage of a reformulation of the Monge-Ampere problem as a saddle-point one, for a well-chosen augmented Lagrangian functional over the product of appropriate primal and dual sets. The convergence of the finite element approximation and of the iterative methods described in this article still has to be proved, however, on the basis of ...

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