Seminar in EDP and Applied Mathematics

september 20, 2023 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Eduardo Casas

Universidad de Cantabria-spain

14:00h – 14:40h

Superlinear Convergence of a Semismooth Newton Method for some Optimization Problems with Applications to Control Theory

Let (X, S, μ) be a measure space with μ(X) < ∞. In this talk, we prove the superlinear convergence of a semismooth Newton method to solve the following abstract optimization problem:
(P) min J(u) +k/2(//u//^2L2(X))
α≤u(x)≤β a.e.[μ]

,where κ > 0, −∞ ≤ α < β ≤ +∞, and J : Lp(X) → R is a function of

class C2 for some p ∈ [2, +∞). Many optimal control problems fall within this abstract formulation, such as distributed or boundary control problems and bilinear control problems associated with nonlinear elliptic or parabolic equations. We propose a superlinearly convergent semismooth Newton method to compute a local minimizer ̄u of (P) assuming that the no-gap second order sufficient optimality condition and the strict complementarity condition are fulfilled.

These assumptions are usually imposed to prove the superlinear or second order convergence of numerical algorithms for solving finite dimensional optimization problems. The translation of our algorithm to the case of optimal control problems governed by elliptic or parabolic semilinear equations is immediate.

Mejdi Azaiez

Bordeaux INP,France

14:50h – 15:30h

Least-Squares Pressure Recovery in Reduced Order Methods for Incompressible Flows

In this talk, we shall introduce a method to recover the reduced
pressure in the Reduced Order Models (ROMs) for incompressible flows. The pressure is obtained via the least-squares minimum of the residual of the reduced velocity with respect to a dual norm. We prove that this procedure provides a unique solution whenever the full-order pair of velocity-pressure spaces is inf-sup stable. We also prove that the proposed method is equivalent to solving the reduced mixed problem with reduced velocity basis enriched with the euphemizers of the reduced pressure gradients. Optimal error estimates for the reduced pressure are obtained for general incompressible flow equations and specifically, for the transient Navier-Stokes equations. We also perform some numerical tests for the flow past a cylinder and the lid-driven cavity flow which confirm the theoretical expectations and show an improved convergence with respect to other pressure recovery methods.

About Organization

Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.