Trivariate Spline Collocation Methods for Numerical Solution to 3D Monge-Ampère Equation

We use trivariate spline functions for the numerical solution of Dirichlet problem 3D elliptic Monge-Ampére equation. Mainly we collocation method introduced in [SIAM J. Numerical Analysis, 2405-2434,2022] to numerically solve iterative Poisson equations and an averaged algorithm ensure convergence iterations. shall also establish rate under a sufficient condition provide some evidence show rates. Then present many computational results demonstrate that this approach works very well. In particular, tested known convex solutions as well nonconvex over domains compared them with several existing methods efficiency effectiveness our approach.