Spline element method for the Monge-Ampere equation
Abstract
We analyze the convergence of an iterative method for solving the nonlinear system resulting from a natural discretization of the Monge-Ampère equation with C1 conforming approximations. We make the assumption, supported by numerical experiments for the two dimensional problem, that the discrete problem has a convex solution. The method we analyze is the discrete version of Newton's method in the vanishing moment methodology. Numerical experiments are given in the framework of the spline element method.
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