Convergence of a hybrid scheme for the elliptic Monge-Ampere equation
Provides a convergent numerical method for the Monge-Ampère equation, a challenging fully nonlinear PDE, but the hybrid approach is incremental.
Proved convergence of a hybrid finite-difference/monotone scheme for the elliptic Monge-Ampère equation to the viscosity solution, addressing the lack of a Newton solver for the standard discretization.
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 discretization in parts of the computational domain where the solution is expected to be smooth and a monotone scheme elsewhere. A motivation for the hybrid discretization is the lack of an appropriate Newton solver for the standard finite difference discretization on the whole domain.