Spline element method for the Monge-Ampere equation. (arXiv:1012.1775v1 [math.NA])

Spline element method for the Monge-Ampere equation. (arXiv:1012.1775v1 [math.NA]): "

We consider numerical approximations of the Monge-Amp\`ere equation det $D^2
u=f, f>0$ with Dirichlet boundary conditions on a convex bounded domain
$\Omega$ in $\mathbb{R}^n, n=2,3$. We make a comparative study of three
existing methods suitable for finite element computations. We construct
conforming approximations in the framework of the spline element method where
constraints and interelement continuities are enforced using Lagrange
multipliers.

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