[NOVA Math] Analysis Seminar

The Center of Mathematics and Applications (NOVA Math) promotes the Seminar of Analysis with the title: "Numerical methods for fully nonlinear degenerate diffusions". Ercília Sousa (Centre for Mathematics of the University of Coimbra (CMUC) & Department of Mathematics of University of Coimbra) is the speaker.

Abstract:  We study a class of degenerate fully nonlinear elliptic equations consisting of a pure equation and an associated transmission-type free boundary problem. We first propose a regularization of the pure equation and derive a numerical method for the regularized problem. The regularization plays a crucial role in ensuring the monotonicity of the numerical scheme. We prove that the method is monotone, consistent, and stable. As a consequence, the Barles–Souganidis framework guarantees the convergence of the numerical approximation. Once the numerical treatment of the pure equation is established, we show how a similar approach can be extended to the free boundary transmission problem. Finally, we present numerical experiments that support the theoretical results.

27 January 2026 (Tuesday), from 14:30 to 15:30, Auditorium Manuel Laranjeira - Building I