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BIRS Workshop Lecture Videos

Generalized finite difference methods for Monge-Ampère equations Froese, Brittany


We introduce a framework for constructing monotone approximations of Monge-Ampère type equations on general meshes or point clouds. These schemes easily handle complex geometries and non-uniform distributions of discretization points. The schemes fit within the Barles-Souganidis convergence framework for approximation of viscosity solutions. However, the PDE itself does not always satisfy the strong form of comparison principle required by this convergence proof. For the Dirichlet problem, which admits non-continuous viscosity solutions, we describe a modified comparison principle that guarantees convergence in the interior of the domain.

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