Emergent Mind
Convergent approaches for the Dirichlet Monge ampère problem
(2301.08636)
Published Jan 20, 2023
in
math.NA
and
cs.NA
Abstract
In this article, we introduce and study three numerical methods for the Dirichlet Monge Amp`ere equation in two dimensions. The approaches consist in considering new equivalent problems. The latter are discretized by a wide stencil finite difference discretization and monotone schemes are obtained. Hence, we apply the Barles-Souganidis theory to prove the convergence of the schemes and the Damped Newtons method is used to compute the solutions of the schemes. Finally, some numerical results are illustrated.
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