Quadratic Finite Element Approximations of the Monge-Ampère Equation

Authors:
Michael Neilan
Affiliations:
Department of Mathematics, University of Pittsburgh, Pittsburgh, USA 15260
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

We prove several new results of the C 0 finite element method introduced in (S.C. Brenner et al., Math. Comput. 80:1979---1995, 2011) for the fully nonlinear Monge-Ampère equation. These include the convergence of quadratic finite element approximations, W 2,p quasi-optimal error estimates, localized pointwise error estimates, and convergence of Newton's method with explicit dependence on the discretization parameter. Numerical experiments are presented which back up the theoretical results.