212 citations · 505 across the 22 of their papers we have counts for
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Discrete Aleksandrov solutions of the Monge-Ampere equation
Gerard Awanou
We prove the convergence of a wide stencil finite difference scheme to the Aleksandrov solution of the elliptic Monge-Ampere equation when the right hand side is a sum of Dirac mas…
Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: mixed methods
Gerard Awanou
We prove a convergence result for a mixed finite element method for the Monge-Ampere equation to its weak solution in the sense of Aleksandrov. The unknowns in the formulation are…
Iterative methods for k-Hessian equations
Gerard Awanou
On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson e…
Quadratic Mixed finite element approximations of the Monge-Ampere equation in 2D
Gerard Awanou
We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampere equation with the unknowns approximated by Lagrange finite elements of…
Convergence of a hybrid scheme for the elliptic Monge-Ampere equation
Gerard Awanou
We prove the convergence of a hybrid discretization to the viscosity solution of the elliptic Monge-Ampere equation. The hybrid discretization uses a standard finite difference dis…