We use trivariate spline functions for the numerical solution of the Dirichlet problem of the 3D
elliptic Monge-Ampére equation. Mainly we use the spline collocation method introduced in …

In this article, we address the numerical solution of the Dirichlet problem for the three-
dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach …

This thesis presents a new collocation method using multivariate splines over triangulation
or tetrahedralization for solving partial differential equations. The method is applied to the …

We review recent advances in the numerical analysis of the Monge–Ampère equation.
Various computational techniques are discussed including wide stencil finite difference …

We analyze the convergence of an iterative method for solving the nonlinear system
resulting from a natural discretization of the Monge–Ampère equation with smooth …

In this paper, we study a spline collocation method for a numerical solution to the optimal
transport problem We mainly solve the\MAE with the second boundary condition numerically …

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic
Monge–Ampère equation using a least-squares/relaxation approach. The relaxation …

We give error estimates for a mixed finite element approximation of the two-dimensional
elliptic Monge–Ampère equation with the unknowns approximated by Lagrange finite …

This thesis focuses on the numerical analysis of partial differential equations (PDEs), the
main goal being the development and analysis of finite element methods (FEMs) for fully …

The proof of Lemma 10 in [Awanou, G.: Quadratic mixed finite element approximations of the
Monge-Ampère equation in 2D. Calcolo 52 (4), 503–518 (2015)] is not correct. The purpose …