# Seminari di Equazioni Differenziali e Applicazioni e discussione di una tesi di dottorato

## Venerdì 8 Aprile 2016, ore 9:30 - Aula 1BC45 - R. Favretti, L. Grüne, L.T.T. Thuy

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Venerdì 8 Aprile 2016 in Aula 1BC45

ore 9:30 Roberto Ferretti (Università di Roma 3) terrà un seminario dal titolo "An adaptive RBF-based Semi-Lagrangian scheme for HJB equations"
Abstract
Semi-Lagrangian (SL) numerical schemes have proved to be an effective and natural strategy for the approximation of Dynamic Programming equations. The construction and approximation properties of SL schemes are crucially related to the choice of a particular space reconstruction operator. In this talk, we will show the construction of an adaptive SL scheme based on a multilevel weighted least squares (Shepard) space reconstruction, whose numerical viscosity is exploited in order to locate the singularities of solutions. We will discuss construction and efficiency of the scheme, and provide some preliminary theoretical analysis, as well as numerical results on control problems in low dimension.

ore 10:30 Lars Grüne (Università di Bayreuth) terrà un seminario del titolo "Value iteration convergence of $\epsilon$-monotone schemes for stationary Hamilton-Jacobi equations".
Abstract
In this talk we consider stationary Hamilton-Jacobi-Bellman equations related to infinite horizon optimal control problems or dynamic games. Our goal is to solve these equations numerically using semi-Lagrangian schemes with high-order discretization in space. While for low order discretizations monotonicity ensures convergence of the value iteration, i.e., termination of the numerical computation, this is in general no longer the case for high-order methods. Main contribution of the talk is to show how $\epsilon$-monotonicity can be used in order to re-establish convergence and to present a selection of high-order schemes to which this theory applies. The talk is based on joint work with Olivier Bokanowski, Maurizio Falcone, Roberto Ferretti, Dante Kalise and Hasnaa Zidani.

ore 11:30 discussione della tesi di Dottorato di Le T.T. Thuy "Results on controllability and the numerical approximation of the minimum time function".
Abstract
My thesis focuses on the unconstrained and constrained minimum time problems, in particular on regularity, numerical approximation, feedback and synthesis aspects.

Rif. Int. M. Bardi, C. Marchi, G. Colombo