A least-squares/relaxation method for the numerical solution of the three-dimensional elliptic Monge-Ampère equation
DOI10.1007/s10915-018-0698-6zbMath1407.65284OpenAlexW2791393583MaRDI QIDQ1632246
Alexandre Caboussat, Dimitrios Gourzoulidis, Roland Glowinski
Publication date: 13 December 2018
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-018-0698-6
Monge-Ampère equationmixed finite element methodleast squares methodNewton methodsnonlinear constrained minimization
Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Monge-Ampère equations (35J96)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal transport for seismic full waveform inversion
- Numerical solution of the optimal transportation problem using the Monge-Ampère equation
- Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations
- A quadratically constrained minimization problem arising from PDE of Monge-Ampère type
- Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
- Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian
- 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
- A class of methods for unconstrained minimization based on stable numerical integration techniques
- Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity
- Finite element approximations of the three dimensional Monge-Ampère equation
- Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
- A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two
- A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes
- Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method
- Solving Ordinary Differential Equations I
- A multigrid scheme for 3D Monge–Ampère equations
- The convex envelope is the solution of a nonlinear obstacle problem
- Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems
- 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
- A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations
- On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order
- Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
- The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
- Two-scale method for the Monge-Ampère equation: Convergence to the viscosity solution
- Optimal Momentum Hedging via Hypoelliptic Reduced Monge--Ampère PDE
- Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
- Exact and Approximate Controllability for Distributed Parameter Systems
- Uniqueness conditions and estimates for the solution of the Dirichlet problem
- The Monge-Ampère equation