Time: 11:00 AM, April 23 (Wednesday)
Place: Room 615 (ASTC)
Speaker: Emilie Pirch (Friedrich Schiller University Jena)
Talk title: Finite element schemes for the Monge-Ampère equation
Abstract: The Monge-Ampère equation is a PDE that arises usually as part of a coupled system of equations and is frequently encountered in the context of transport or curvature problems. It is fully non-linear, degenerate elliptic and in non-divergence form and a special constraint is that the solution needs to be convex. All of these properties make it challenging to solve the Monge-Ampère equation numerically, as they are not intuitive with standard solution techniques, and recent advances in the numerical analysis of this PDE will be the subject of this talk. In particular, some finite element schemes using a regularization will be presented and one of the aims is to find an error estimator that allows adaptive computation with a mixed formulation. Furthermore, difficulties that arise from the limited availability of analytical tools will be discussed.
Contact: Eun-Jae Park, ejpark@yonsei.ac.kr