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

2013/01/24 by Gerard Awanou, Awanou, Gerard
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.1301.5891

openalex publication_date 2013/01/24 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We present two numerical methods for the fully nonlinear elliptic\nMonge-Ampere equation. The first is a pseudo transient continuation method and\nthe second is a pure pseudo time marching method. The methods are proven to\nconverge to a strictly convex solution of a natural discrete variational\nformulation with C¹ conforming approximations. The assumption of existence\nof a strictly convex solution to the discrete problem is proven for smooth\nsolutions of the continuous problem and supported by numerical evidence for non\nsmooth solutions.\n

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Convergence Analysis of Pseudo-Transient Continuation
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• Spline element method for the Monge-Ampere equation

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