Numerical Methods with Convergence Rates for the Monge-Ampere Equation
Prof. Ricardo H. Nochetto, University of Maryland
Aula Beltrami, Dipartimento di Matematica – Lunedì 20 Gennaio 2020 h.14:15
Abstract. We analyze the Oliker-Prussner method and a two-scale method for the Monge-Ampere equation with Dirichlet boundary condition, and explore connections with a Bellman formulation. We also study a two-scale method for a fully nonlinear obstacle problem associated with convex envelopes. We derive pointwise error estimates that rely on the discrete Alexandroff maximum principle and the geometric structure of these PDEs for both classical and non-classical solutions.