Numerical solution of the simple Monge–Ampère equation with nonconvex dirichlet data on non-convex domains

Jensen, Max (2018) Numerical solution of the simple Monge–Ampère equation with nonconvex dirichlet data on non-convex domains. In: Dante, Kalise, Kunisch, Karl and Zhiping, Rao (eds.) Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control. Radon Series on Computational and Applied Mathematics . De Gruyter, Berlin,, pp. 129-142. ISBN 9783110543599 (Accepted)

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Abstract

The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampere equation is known independently of the convexity of the domain or Dirichlet boundary data - when the Monge-Ampere equation is posed as a Bellman problem. However, the convergence to the viscosity solution has only been proved on strictly convex domains. In this paper, we provide numerical evidence that convergence of numerical solutions is observed more generally without convexity assumptions. We illustrate how in the limit multivalued functions may be approximated to satisfy the Dirichlet conditions on the boundary as well as local convexity in the interior of the domain

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
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Depositing User: Max Jensen
Date Deposited: 20 Feb 2018 12:51
Last Modified: 17 Aug 2018 07:55
URI: http://sro.sussex.ac.uk/id/eprint/73725

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