Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type
DOI10.1016/j.cma.2005.05.023zbMath1119.65116OpenAlexW2054715051MaRDI QIDQ2372475
Edward J. Dean, Roland Glowinski
Publication date: 27 July 2007
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2005.05.023
Dirichlet problemnumerical experimentsnonlinear elasticityelliptic equationssaddle-point problemmixed finite elementMonge-Ampère equationsoperator-splittingnonlinear least-squaresPucci's equationsUzawa-Douglas-Rachford algorithm
Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
- An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
- 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
- On the numerical analysis of the Von Kármán equations: Mixed finite element approximation and continuation techniques
- Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: An augmented Lagrangian approach
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- Finite-element Approximations and Iterative Solutions of a Fourth-order Elliptic Variational Inequality
- Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems
- A modular system of algorithms for unconstrained minimization
- The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
- The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes Problem
- Mixed and Hybrid Finite Element Methods
- Product formulas and numerical algorithms
- Monge Ampère Equation: Applications to Geometry and Optimization
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