The Monge-Ampère equation: various forms and numerical solution

DOI10.1016/j.jcp.2010.03.025zbMath1194.65141arXiv0910.1301OpenAlexW2154185329MaRDI QIDQ982963

Vladislav Zheligovsky, Uriel Frisch, Olga M. Podvigina

Publication date: 28 July 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1301

zbMATH Keywords

convergencenumerical examplesiterative methodsMonge-Ampère equationFourier integral form

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Monge-Ampère equations (35J96)

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Cites Work

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• The Monge-Ampère-Kantorovich approach to reconstruction in cosmology
• An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
• On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I
• An optimized iterative method for numerical solution of large systems of equations based on the extremal property of zeroes of Chebyshev polynomials
• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: An augmented Lagrangian approach
• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: a least-squares approach
• Numerical solution of the Monge--Ampère equation by a Newton's algorithm
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type
• Optimal mass transport for registration and warping
• Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
• Two Numerical Methods for the elliptic Monge-Ampère equation
• Iterative Solution Methods
• The Monge-Ampère equation