An efficient approach for the numerical solution of the Monge-Ampère equation
type: Item
instance of: scholarly article
title: An efficient approach for the numerical solution of the Monge-Ampère equation
zbMATH Open document ID: 1215.65178
author: Juan-Miguel Gracia
published in: Applied Numerical Mathematics
publication date: 2011-02-11T00:00:00Z
review text: The authors present an alternative method to compute the numerical solution of the elliptic Monge-Ampère equation \[ \rho _1\left( \nabla \Psi \left( \xi \right) \right) \det \nabla ^2\Psi \left( \xi \right) =\rho _0\left( \xi \right). \] The alternative aproach is based on finding a steady-state solution of the logarithmic parabolic Monge-Ampère equation \[ \frac{\partial \Psi }{\partial t} = \log \left( \frac{\rho _1\left( \nabla \Psi \left( \xi \right) \right) \det \nabla ^2\Psi \left( \xi \right) }{\rho _0\left( \xi \right) }\right), \] together with some suitable initial and boundary conditions. The authors study the problem of global existence, uniqueness and convergence of the solution of the fully nonlinear parabolic equation to the unique solution of the elliptic Monge-Ampère equation. Some numerical experiments illustrate the convergence and the regularity of the numerical solution.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J96
Mathematics Subject Classification ID: 35K96
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 5850232
zbMATH Keywords: global existence
zbMATH Keywords: convergence
zbMATH Keywords: elliptic Monge-Ampère equation
zbMATH Keywords: logarithmic parabolic Monge-Ampère equation
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.10.006
OpenAlex ID: W1964250113
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DOI: 10.1016/J.APNUM.2010.10.006
description: scientific article; zbMATH DE number 5850232