Spline element method for the Monge-Ampere equation

2010/12/08 by Gerard Awanou, Awanou, Gerard · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1012.1775

openalex publication_date 2010/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the convergence of an iterative method for solving the nonlinear system resulting from a natural discretization of the Monge-Ampère equation with C¹ conforming approximations. We make the assumption, supported by numerical experiments for the two dimensional problem, that the discrete problem has a convex solution. The method we analyze is the discrete version of Newton's method in the vanishing moment methodology. Numerical experiments are given in the framework of the spline element method.

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• The finite element method with Lagrangian multipliers
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation

Cited by

• Pseudo transient continuation and time marching methods for Monge-Ampere\n type equations

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