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The elliptic Monge-Amp\`ere equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community.
On the approximation of linear elliptic differential equations by difference equations with positive coefficients
T. S. Motzkin and W. Wasow · 1952
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Multi-level adaptive solutions to boundary-value problems
A. Brandt · 1977
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The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation
L. Caffarelli, L. Nirenberg, and J. Spruck · 1984
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Convergence of approximation schemes for fully nonlinear second order equations
G. Barles and P. E. Souganidis · 1991
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Fast and high accuracy multigrid solution of the three-dimensional Poisson equation
J. Zhang · 1998
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A multigrid tutorial
W. L. Briggs, V. E. Henson, and S. F. McCormick · 2000
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High accuracy multigrid solution of the 3D convection-diffusion equation
M. M. Gupta and J. Zhang · 2000
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Iterative solution of nonlinear equations in several variables
J. M. Ortega and W. C. Rheinboldt · 2000
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Multigrid
U. Trottenberg, C. W. Oosterlee, and A. Schüller · 2001
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Iterative methods for sparse linear systems
Y. Saad · 2003
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Optimal mass transport for registration and warping
S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent · 2004
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Numerical solution of the Monge-Ampère equation by a Newton’s algorithm
G. Loeper and F. Rapetti · 2005
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Image registration with guaranteed displacement regularity
E. Haber and J. Modersitzki · 2007
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Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems
R. LeVeque · 2007
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An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge–Kantorovich optimization
G. L. Delzanno, L. Chacón, J. M. Finn, Y. Chung, and G. Lapenta · 2008
Cited alongside, same era.
Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian
A. M. Oberman · 2008
Cited alongside, same era.
The Monge-Ampere equation and its geometric applications
N. S. Trudinger and X.-J. Wang · 2008
Cited alongside, same era.
Mixed finite element methods for the fully nonlinear Monge-Ampère equation based on the vanishing moment method
X. Feng and M. Neilan · 2009
Cited alongside, same era.
Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations
X. Feng and M. Neilan · 2009
Cited alongside, same era.
Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher
B. D. Froese and A. M. Oberman · 2011
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Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
B. D. Froese and A. M. Oberman · 2011
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Multigrid for Elliptic Monge-Ampère Equation
A. K. Soin · 2011
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An efficient approach for the numerical solution of the Monge-Ampère equation
M. M. Sulman, J. F. Williams, and R. D. Russell · 2011
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Finite element approximations of the three dimensional Monge-Ampère equation
S. C. Brenner and M. Neilan · 2012
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A review of numerical methods for nonlinear partial differential equations
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3d nonrigid registration via optimal mass transport on the GPU
E. Haber, G. Pryor, J. Melonakos, A. Tannenbaum, et al · 2009
Cited alongside, same era.
Two numerical methods for the elliptic Monge-Ampère equation
J.-D. Benamou, B. D. Froese, and A. M. Oberman · 2010
Cited alongside, same era.
An adaptive continuation-multigrid method for the balanced vortex model
Y. Chen and S. R. Fulton · 2010
Cited alongside, same era.
An efficient numerical method for the solution of the L 2 {L}_{2} optimal mass transfer problem
E. Haber, T. Rehman, and A. Tannenbaum · 2010
Cited alongside, same era.
The Monge-Ampère equation: Various forms and numerical solution
V. Zheligovsky, O. Podvigina, and U. Frisch · 2010
Cited alongside, same era.
Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition
A. Brandt and O. Livne · 2011
Cited alongside, same era.
C 0 C^{0} penalty methods for the fully nonlinear Monge-Ampère equation
S. C. Brenner, T. Gudi, M. Neilan, and L.-y. Sung · 2011
Cited alongside, same era.
E. Tadmor · 2012
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Recent developments in numerical methods for fully nonlinear second order partial differential equations
X. Feng, R. Glowinski, and M. Neilan · 2013
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Convergent filtered schemes for the Monge-Ampère partial differential equation
B. D. Froese and A. M. Oberman · 2013
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Quadratic finite element approximations of the Monge-Ampère equation
M. Neilan · 2013
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Numerical solution of the optimal transportation problem using the Monge-Ampère equation
J.-D. Benamou, B. D. Froese, and A. M. Oberman · 2014
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Application of the Wasserstein metric to seismic signals
B. Engquist and B. D. Froese · 2014
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A Monge-Ampère-solver for free-form reflector design
C. R. Prins, J. H. M. Ten Thije Boonkkamp, J. van Roosmalen, W. L. Ijzerman, and T. W. Tukker · 2014
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An efficient numerical algorithm for the L 2 L^{2} optimal transport problem with periodic densities
L.-P. Saumier, M. Agueh, and B. Khouider · 2015
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