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Advanced FEM techniques

This is an advanced monographic course on the numerical analysis of PDEs using state-of-the-art nonconforming and discontinuous finite element methods. This will include very recent research on the development of methods on extremely general meshes, such as virtual elements and discontinuous Galerkin methods.  Topics

Numerical Solution of PDEs

This course provides a high level overview on the numerical solution of partial differential equations. All major classes of numerical methods will be analysed within a rigorous mathematical setting. Key aspects, such as consistency and stability, will be thoroughly investigated, providing the guidelines for the correct choice and implementation of numerical methods for a range of problems.

AJS - Analysis Junior Seminars 2020-2021

Date Speaker Seminar
October 9 Nicolò De Ponti New results on Buser's and Cheeger's inequalities
October 16 Giorgio Saracco Structure of minimizers of the (planar) prescribed curvature functional
October 23 Monica Nonino Segregated Reduced Order Models for Fluid-Strucutre Interaction problems
October 30 Ruijun Wu Super Liouville systems on Riemann surfaces
November 6 Lorenzo Portinale Discrete-to-Continuum Limits of Transport Problems and Gradient-Flow Evolutions
November 13 Francesco Nobili A differential perspective on gradient flows on CAT(0) spaces and applications
November 20 Maria Strazzullo Driving Nonlinear Bifurcating Phenomena by Optimal Control: an application to Navier-Stokes Equations
November 27 Sara Farinelli The size of nodal sets in singular spaces via indeterminacy estimates
December 4 Michele Dolce An example of mixing and enhanced dissipation in the whole plane
December 11 Tommaso Rossi Heat content asymptotics for sub-Riemannian manifolds
December 18 Eleonora Piersanti Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity
January 15 Giuliano Klun Well-ordered and non-well-ordered lower and upper solutions for periodic planar systems
January 22 Umberto Morelli Real-time estimation of the steel-mold heat flux in continuous casting
February 5 Francesca Cairoli Abstraction of Markov Population Dynamics via Generative Adversarial Nets
February 12 Martina Cracco Linear stability and transient behaviour of viscoelastic fluids in boundary layers
February 19 Federico Pichi Artificial neural network for bifurcating phenomena modelled by nonlinear parametrized PDEs
February 26 Riccardo Tione On the Commutativity of Flows of Rough Vector Fields
March 12 Gennaro Ciampa Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit
March 18 Elio Marconi Differentiability properties of flows of planar autonomous vector fields
March 19 Youngsoo Choi Where are we with data-driven surrogate modeling for various physical simulations?
March 26 Elisa Fevola Optimal Control for Boundary Conditions Estimation in Cardiovascular Modeling
April 9 Martina Teruzzi Digital twins and graph theory: a parallel fault-simulation software with naval applications
April 16 Anna Nikishova Uncertainty quantification of multiscale models
April 30 Alessandro Carbotti Recent developments on fractional perimeters in Gauss space
May 7 Giuliano Klun On Dini derivatives of real functions
May 28 Matteo Zancanaro Closure models for reduced order methods compressible flows approaches: a balance between consolidation and innovation
June 4 Ivan Yuri Violo Monotonicity formula for harmonic functions in RCD(0,N) spaces
June 25 Beatrice Langella Growth of Sobolev norms for unbounded perturbations of the Laplacian on flat tori
September 23 Paolo Ventura Full description of Benjamin-Feir instability of Stokes waves in deep water

Advanced Programming

The course aims to provide advanced knowledge of both theoretical and practical programming in C++11 and Python3, with particular regard to the principles of object-oriented programming and best practices of software development.

Due to covid-19 containement rules, this year, videos with pre-recorded lectures will be uploaded weekly, starting from the week of October 5, 2020.

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