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

Jensen, Max (2018) Numerical solution of the simple Monge–Ampère equation with non-convex dirichlet data on non-convex domains. Numerical methods for Hamilton-Jacobi equations in optimal control and related fields, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, 21-25 November 2016. Published in: Dante, Kalise, Kunisch, Karl and Zhiping, Rao, (eds.) Hamilton-Jacobi-Bellman Equations. De Gruyter ISBN 9783110543599 (Accepted)

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Abstract

The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge–Ampère equation is known independently of the convexity of the domain or Dirichlet boundary data—when the Monge–Ampère equation is posed as Bellman problem. However, the convergence to the viscosity solution has only been proved on strictly convex do- mains. 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 multi- valued 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: Conference Proceedings
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
Depositing User: Max Jensen
Date Deposited: 20 Feb 2018 12:51
Last Modified: 21 Feb 2018 16:35
URI: http://sro.sussex.ac.uk/id/eprint/73725

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