Title	Generalized finite difference methods for Monge-Ampère equations
Creator	Froese, Brittany
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-04-10T15:42
Description	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.
Extent	53 minutes
Subject	Mathematics; Partial differential equations; Calculus of variations and optimal control; optimization
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: New Jersey Institute of Technology
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-10-08
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0356568
URI	http://hdl.handle.net/2429/63218
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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

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