Add to ORKGIn this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings. © EDP Sciences, SMAI, 2012
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monoto...
Abstract. The goal of this work is to illustrate the application of the nonvari-ational finite eleme...
We introduce a monotone (degenerate elliptic) discretization of the Monge−Ampere operator,...
In this paper, we construct and analyze finite element methods for the three dimensional M...
Abstract. We analyze the convergence of a mixed finite element method for the elliptic Monge-Ampère...
Abstract. We consider numerical approximations of the Monge-Ampère equation det D2u = f, f> 0 wi...
Abstract. We propose a new variational formulation of the elliptic Monge-Ampère equation and show h...
Abstract. This paper develops and analyzes finite element Galerkin and spectral Galerkin meth-ods fo...
In this article, we address the numerical solution of the Dirichlet problem for the three-dimensiona...
We prove a convergence result for a natural discretization of the Dirichlet problem of the elliptic ...
We introduce a framework for constructing monotone approximations of Monge-Ampère type equations on ...
In this paper, we develop and analyze C penalty methods for the fully nonlinear Monge-Ampère equatio...
In this article, we report the results we obtained when investigating the numerical solution of some...
We design a monotone finite difference discretization of the second boundary value problem for the M...
In this article, we address the numerical solution of the Dirichlet problem for the three-dimensiona...
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monoto...
Abstract. The goal of this work is to illustrate the application of the nonvari-ational finite eleme...
We introduce a monotone (degenerate elliptic) discretization of the Monge−Ampere operator,...
In this paper, we construct and analyze finite element methods for the three dimensional M...
Abstract. We analyze the convergence of a mixed finite element method for the elliptic Monge-Ampère...
Abstract. We consider numerical approximations of the Monge-Ampère equation det D2u = f, f> 0 wi...
Abstract. We propose a new variational formulation of the elliptic Monge-Ampère equation and show h...
Abstract. This paper develops and analyzes finite element Galerkin and spectral Galerkin meth-ods fo...
In this article, we address the numerical solution of the Dirichlet problem for the three-dimensiona...
We prove a convergence result for a natural discretization of the Dirichlet problem of the elliptic ...
We introduce a framework for constructing monotone approximations of Monge-Ampère type equations on ...
In this paper, we develop and analyze C penalty methods for the fully nonlinear Monge-Ampère equatio...
In this article, we report the results we obtained when investigating the numerical solution of some...
We design a monotone finite difference discretization of the second boundary value problem for the M...
In this article, we address the numerical solution of the Dirichlet problem for the three-dimensiona...
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monoto...
Abstract. The goal of this work is to illustrate the application of the nonvari-ational finite eleme...
We introduce a monotone (degenerate elliptic) discretization of the Monge−Ampere operator,...