Seminars & Colloquia Calendar
Generalized finite difference methods for fully nonlinear elliptic equations
Brittany Hamfeldt, NJIT
Location: Hill 425
Date & time: Friday, 20 September 2019 at 12:00PM - 1:00PM
Abstract: The introduction of viscosity solutions and the Barles-Souganidis convergence framework have allowed for considerable progress in the numerical solution of fully nonlinear elliptic equations. We describe a framework for constructing convergent generalised finite difference approximations for a large class of nonlinear elliptic operators. These approximations are defined on unstructured point clouds, which allows for computation on non-uniform meshes and complicated geometries. Because the schemes are monotone, they fit within the Barles-Souganidis convergence framework and can serve as a foundation for higher-order filtered methods. We present computational results for several examples including problems posed on random point clouds, examples incorporating automatic mesh adaptation, non-continuous surfaces of prescribed Gaussian curvature, Monge-Ampere equations arising in optimal transportation, and Monge-Ampere type equations on the sphere.