A CONVERGENT FINITE DIFFERENCE METHOD FOR COMPUTING MINIMAL LAGRANGIAN GRAPHS

Document Type

Article

Publication Date

2-1-2022

Abstract

We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an additive eigenvalue problem for a fully nonlinear elliptic partial differential equation. We introduce and implement a two-step generalized finite difference method, which we prove converges to the solution of the eigenvalue problem. Numerical experiments validate this approach in a range of challenging settings. We further discuss the generalization of this new framework to Monge-Ampère type equations arising in optimal transport. This approach holds great promise for applications where the data does not naturally satisfy the mass balance condition, and for the design of numerical methods with improved stability properties.

Identifier

85123839747 (Scopus)

Publication Title

Communications on Pure and Applied Analysis

External Full Text Location

https://doi.org/10.3934/CPAA.2021182

e-ISSN

15535258

ISSN

15340392

First Page

393

Last Page

418

Issue

2

Volume

21

Grant

DMS-1751996

Fund Ref

National Science Foundation

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