Spline element method for the Monge-Ampere equation

Details Spline element method for the Monge-Ampere equation Spline element method for the Monge-Ampere equation

2010-12-08

arxiv.org/abs/1012.1775v1

Mathematics

Numerical Analysis

Scientific paper

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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