212 citations · 505 across the 22 of their papers we have counts for
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On standard finite difference discretizations of the elliptic Monge-Ampere equation
Gerard Awanou
Given an orthogonal lattice with mesh length h on a bounded convex domain, we propose to approximate the Aleksandrov solution of the Monge-Ampere equation by regularizing the data…
Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: classical solutions
Gerard Awanou
We propose a new variational formulation of the elliptic Monge-Ampere equation and show how classical Lagrange elements can be used for the numerical resolution of classical soluti…
Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: Aleksandrov solutions
Gerard Awanou
We prove a convergence result for a natural discretization of the Dirichlet problem of the elliptic Monge-Ampere equation using finite dimensional spaces of piecewise polynomial C0…
Mixed finite elements for elasticity on quadrilateral meshes
Douglas N. Arnold, Gerard Awanou, Weifeng Qiu
We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three pri…
Pseudo transient continuation and time marching methods for Monge-Ampere type equations
Gerard Awanou
We present two numerical methods for the fully nonlinear elliptic Monge-Ampere equation. The first is a pseudo transient continuation method and the second is a pure pseudo time ma…