Numerical solution of the two-dimensional elliptic Monge-Ampère equation with Dirichlet boundary conditions: an augmented Lagrangian approach

By Edward J. Dean, Roland Glowinski. 2003

69 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Surgery

View Paper: https://www.semanticscholar.org/paper/24f338b047bb35044800a96b415090a82178a0e7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Weizhang Huang
2. Robert D. Russell
3. Francesca Rapetti
4. Chris J. Budd
5. Adam M. Oberman
6. Grégoire Loeper
7. Alessio Figalli
8. Cédric Villani

In Geometry and Topology

1. Weizhang Huang
2. Robert D. Russell
3. Francesca Rapetti
4. Chris J. Budd
5. Adam M. Oberman
6. Grégoire Loeper
7. Alessio Figalli
8. Robert J. McCann

In Surgery

1. Francesca Rapetti
2. Adam M. Oberman
3. Grégoire Loeper

Citations in the corpus

• Numerical Analysis/Partial Differential Equations Numerical solution of the Monge-Ampère equation by a Newton's algorithm (2005, methodology): “The convergence of the method is not guaranteed for non-smooth right-hand side and alternative approaches are proposed in [1, 5 ,6,8].”
• Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian (2008, methodology): “Recently, Dean and Glowinksi have investigated numerical methods for the Monge-Ampère equation [8, 7, 6, 10] and Pucci’s equations [9].”
• Adaptivity with moving grids (2009, background): “Dean and Glowinski (2003, 2004) propose finite element discretizations based on an augmented Lagrangian approach and a least-squares formulation respectively.”