On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator

Roland GLOWINSKI, Shingyu Leung, Hao Liu*, Jianliang Qian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we report the results we obtained when investigating the numerical solution of some nonlinear eigenvalue problems for the Monge-Ampère operator v → det D2v. The methodology we employ relies on the following ingredients: (i) a divergence formulation of the eigenvalue problems under consideration. (ii) The time discretization by operator-splitting of an initial value problem (a kind of gradient flow) associated with each eigenvalue problem. (iii) A finite element approximation relying on spaces of continuous piecewise affine functions. To validate the above methodology, we applied it to the solution of problems with known exact solutions: The results we obtained suggest convergence to the exact solution when the space discretization step h → 0. We considered also test problems with no known exact solutions.

Original languageEnglish
Article number118
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume26
DOIs
Publication statusPublished - 2020

Scopus Subject Areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

User-Defined Keywords

  • Finite element approximations
  • Monge-Ampère equation
  • Nonlinear eigenvalue problems
  • Operator-splitting methods

Fingerprint

Dive into the research topics of 'On the numerical solution of nonlinear eigenvalue problems for the Monge-Ampère operator'. Together they form a unique fingerprint.

Cite this