A finite element/operator-splitting method for the numerical solution of the two dimensional elliptic Monge-Ampère equation

DOI10.1007/s10915-018-0839-yzbMath1447.65141OpenAlexW2893817145MaRDI QIDQ2000024

Hao Liu, Shingyu Leung, Jianliang Qian, Roland Glowinski

Publication date: 27 June 2019

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-018-0839-y

zbMATH Keywords

mixed finite element methodsfinite element approximationsMonge-Ampère equationsoperator-splitting methodfully nonlinear elliptic partial differential equationsvariational crimesTychonoff regularization

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Monge-Ampère equations (35J96)

Related Items (13)

Computing the finite time Lyapunov exponent for flows with uncertainties ⋮ Numerical Identification of Nonlocal Potentials in Aggregation ⋮ Neighbor-gradient single-pass method for solving anisotropic eikonal equation ⋮ An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging ⋮ Fast operator splitting methods for obstacle problems ⋮ Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation ⋮ Elastica Models for Color Image Regularization ⋮ Cascadic Newton’s method for the elliptic Monge–Ampère equation ⋮ A Second Order Time Integration Method for the Approximation of a Parabolic 2D Monge-Ampère Equation ⋮ Unnamed Item ⋮ A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation ⋮ On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator ⋮ A Color Elastica Model for Vector-Valued Image Regularization

Uses Software

• DistMesh

Cites Work

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