Papers › A finite element method for the Monge--Ampère equation with transport boundary conditions
A finite element method for the Monge--Ampère equation with transport boundary conditions
Ellya Kawecki, Omar Lakkis, Tristan Pryer
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We address the numerical solution via Galerkin type methods of the Monge-Amp\`ere equation with transport boundary conditions arising in optimal mass transport, geometric optics and computational mesh or grid movement techniques. This fully nonlinear elliptic problem admits a linearisation via a Newton-Raphson iteration, which leads to an oblique derivative boundary value problem for elliptic equations in nondivergence form. We discretise these by employing the nonvariational finite element method, which lead to empirically observed optimal convergence rates, provided recovery techinques are used to approximate the gradient and the Hessian of the unknown functions. We provide extensive numerical testing to illustrate the strengths of our approach and the potential applications in optics and mesh movement.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections