5 citations · 6 across the 4 of their papers we have counts for
9 papers
On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations
Gerard Awanou, Gantumur Tsogtgerel
We prove that two Aleksandrov solutions of a generated prescribed Jacobian equation have the same gradients at points where they are both differentiable. For the optimal transporta…
Hybridization and postprocessing in finite element exterior calculus
Gerard Awanou, Maurice Fabien, Johnny Guzmán +1
We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential -forms in . In the cases and , we recover…
Convergence of a damped Newton's method for discrete Monge-Ampere functions with a prescribed asymptotic cone
Gerard Awanou
For finite difference discretizations with linear complexity and provably convergent to weak solutions of the second boundary value problem for the Monge-Ampère equation, we give t…
The second boundary value problem for a discrete Monge-Ampere equation
Gerard Awanou
In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we pro…
On weak convergence of Monge-Ampere measures for discrete convex mesh functions
Gerard Awanou
To a mesh function we associate the natural analogue of the Monge-Ampere measure. The latter is shown to be equivalent to the Monge-Ampere measure of the convex envelope. We prove…
Uniform limit of discrete convex functions
Gerard Awanou
We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded…