Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation

Hao Liu, Roland Glowinski, Shingyu Leung and Jianliang Qian
Journal of Scientific Computing 81 (3) 2271 (2019)
DOI: 10.1007/s10915-019-01080-4
See this article

Quadratic Finite Element Approximations of the Monge-Ampère Equation

Michael Neilan
Journal of Scientific Computing 54 (1) 200 (2013)
DOI: 10.1007/s10915-012-9617-4
See this article

Numerical analysis of strongly nonlinear PDEs

Michael Neilan, Abner J. Salgado and Wujun Zhang
Acta Numerica 26 137 (2017)
DOI: 10.1017/S0962492917000071
See this article

Splitting Methods in Communication, Imaging, Science, and Engineering

Roland Glowinski
Scientific Computation, Splitting Methods in Communication, Imaging, Science, and Engineering 251 (2016)
DOI: 10.1007/978-3-319-41589-5_8
See this article

Numerical methods for the 2-Hessian elliptic partial differential equation

Brittany D. Froese, Adam M. Oberman and Tiago Salvador
IMA Journal of Numerical Analysis 37 (1) 209 (2017)
DOI: 10.1093/imanum/drw007
See this article

A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two

Alexandre Caboussat, Roland Glowinski and Danny C. Sorensen
ESAIM: Control, Optimisation and Calculus of Variations 19 (3) 780 (2013)
DOI: 10.1051/cocv/2012033
See this article

Spline element method for Monge–Ampère equations

Gerard Awanou
BIT Numerical Mathematics 55 (3) 625 (2015)
DOI: 10.1007/s10543-014-0524-y
See this article

Monotone and consistent discretization of the Monge-Ampère operator

Jean-David Benamou, Francis Collino and Jean-Marie Mirebeau
Mathematics of Computation 85 (302) 2743 (2016)
DOI: 10.1090/mcom/3080
See this article

Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations

Xiaobing Feng, Roland Glowinski and Michael Neilan
SIAM Review 55 (2) 205 (2013)
DOI: 10.1137/110825960
See this article

Numerical Mathematics and Advanced Applications ENUMATH 2019

Alexandre Caboussat and Dimitrios Gourzoulidis
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2019 139 225 (2021)
DOI: 10.1007/978-3-030-55874-1_21
See this article

Pseudo transient continuation and time marching methods for Monge-Ampère type equations

Gerard Awanou
Advances in Computational Mathematics 41 (4) 907 (2015)
DOI: 10.1007/s10444-014-9391-y
See this article

Modeling, Simulation and Optimization for Science and Technology

Alexandre Caboussat
Computational Methods in Applied Sciences, Modeling, Simulation and Optimization for Science and Technology 34 23 (2014)
DOI: 10.1007/978-94-017-9054-3_2
See this article

Three ways to solve partial differential equations with neural networks — A review

Jan Blechschmidt and Oliver G. Ernst
GAMM-Mitteilungen 44 (2) (2021)
DOI: 10.1002/gamm.202100006
See this article

A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains

Susanne C. Brenner, Li-yeng Sung, Zhiyu Tan and Hongchao Zhang
Numerische Mathematik 148 (3) 497 (2021)
DOI: 10.1007/s00211-021-01210-x
See this article

A multigrid scheme for 3D Monge–Ampère equations

Jun Liu, Brittany D. Froese, Adam M. Oberman and Mingqing Xiao
International Journal of Computer Mathematics 94 (9) 1850 (2017)
DOI: 10.1080/00207160.2016.1247443
See this article

Error estimation for second‐order partial differential equations in nonvariational form

Jan Blechschmidt, Roland Herzog and Max Winkler
Numerical Methods for Partial Differential Equations 37 (3) 2190 (2021)
DOI: 10.1002/num.22678
See this article

A DGFEM for nondivergence form elliptic equations with Cordes coefficients on curved domains

Ellya L. Kawecki
Numerical Methods for Partial Differential Equations 35 (5) 1717 (2019)
DOI: 10.1002/num.22372
See this article

Two-scale method for the Monge–Ampère equation: pointwise error estimates

R H Nochetto, D Ntogkas and W Zhang
IMA Journal of Numerical Analysis 39 (3) 1085 (2019)
DOI: 10.1093/imanum/dry026
See this article

Solving the Monge–Ampère equations for the inverse reflector problem

Kolja Brix, Yasemin Hafizogullari and Andreas Platen
Mathematical Models and Methods in Applied Sciences 25 (05) 803 (2015)
DOI: 10.1142/S0218202515500190
See this article

Optimal Pointwise Error Estimates for Two-Scale Methods for the Monge--Ampère Equation

Wenbo Li and Ricardo H. Nochetto
SIAM Journal on Numerical Analysis 56 (3) 1915 (2018)
DOI: 10.1137/18M1165670
See this article

Discretization of the 3d monge−ampere operator, between wide stencils and power diagrams

Jean-Marie Mirebeau
ESAIM: Mathematical Modelling and Numerical Analysis 49 (5) 1511 (2015)
DOI: 10.1051/m2an/2015016
See this article

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge–Ampère Equation

Roland Glowinski, Hao Liu, Shingyu Leung and Jianliang Qian
Journal of Scientific Computing 79 (1) 1 (2019)
DOI: 10.1007/s10915-018-0839-y
See this article

Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements

Andrew T. T. McRae, Colin J. Cotter and Chris J. Budd
SIAM Journal on Scientific Computing 40 (2) A1121 (2018)
DOI: 10.1137/16M1109515
See this article

Pointwise rates of convergence for the Oliker–Prussner method for the Monge–Ampère equation

Ricardo H. Nochetto and Wujun Zhang
Numerische Mathematik 141 (1) 253 (2019)
DOI: 10.1007/s00211-018-0988-9
See this article

A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems

Ellya L. Kawecki
SIAM Journal on Numerical Analysis 57 (2) 751 (2019)
DOI: 10.1137/17M1155946
See this article

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge–Ampère Equation

Alexandre Caboussat, Roland Glowinski and Dimitrios Gourzoulidis
Journal of Scientific Computing 77 (1) 53 (2018)
DOI: 10.1007/s10915-018-0698-6
See this article

A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation

Hongtao Chen, Xiaobing Feng and Zhimin Zhang
Advances in Computational Mathematics 47 (2) (2021)
DOI: 10.1007/s10444-021-09847-w
See this article

A high-order numerical scheme for stochastic optimal control problem

Yunzhang Li
Journal of Computational and Applied Mathematics 427 115158 (2023)
DOI: 10.1016/j.cam.2023.115158
See this article

Geometric Partial Differential Equations - Part I

Michael Neilan, Abner J. Salgado and Wujun Zhang
Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part I 21 105 (2020)
DOI: 10.1016/bs.hna.2019.05.003
See this article