Abstract:
Variational formulations are a popular tool to analyse linear PDEs (eg. neutron diffusion, Maxwell equations, Stokes equations ...), and it also provides a convenient basis to design numerical methods to solve them. Of paramount importance is the inf-sup condition, designed by Ladyzhenskaya, Necas, Babuska and Brezzi in the 1960s and 1970s. As is well-known, it provides sharp conditions to prove well-posedness of the problem, namely existence and uniqueness of the solution, and continuous dependence with respect to the data. Then, to solve the approximate, or discrete, problems, there is the (uniform) discrete inf-sup condition, to ensure existence of the approximate solutions, and convergence of those solutions to the exact solution. Often, the two sides of this problem (exact and approximate) are handled separately, or at least no explicit connection is made between the two.In this talk, I will focus on an approach that is completely equivalent to the inf-sup condition for problems set in Hilbert spaces, the T-coercivity approach. This approach relies on the design of an explicit operator to realize the inf-sup condition. If the operator is carefully chosen, it can provide useful insight for a straightforward definition of the approximation of the exact problem. As a matter of fact, the derivation of the discrete inf-sup condition often becomes elementary, at least when one considers conforming methods, that is when the discrete spaces are subspaces of the exact Hilbert spaces. In this way, both the exact and the approximate problems are considered, analysed and solved at once.In itself, T-coercivity is not a new theory, however it seems that some of its strengths have been overlooked, and that, if used properly, it can be a simple, yet powerful tool to analyse and solve linear PDEs. In particular, it provides guidelines such as, which abstract tools and which numerical methods are the most “natural” to analyse and solve the problem at hand. In other words, it allows one to select simply appropriate tools in the mathematical, or numerical, toolboxes. This claim will be illustrated on classical linear PDEs, and for some generalizations of those models.

16:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 35/36

ETH Zürich

DACO Seminar

Sabrina Bruckmeier (ETH Zürich, Switzerland)

Constrained Sparse Approximation over the Cube abstract

17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2

Thursday, May 25

ETH Zürich

Nachdiplomvorlesung

Brita Nucinkis (Royal Holloway, University of London)

Cohomological methods in group theory

10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

EPF Lausanne

Computational Science and Engineering

Prof. Dr. Piotr Indyk (MIT)

Faster Kernel Matrix Algebra via Density Estimation abstract

13:00 • EPF Lausanne, Salle GA 3 21

EPF Lausanne

Groups, Arithmetic and Algebraic Geometry Seminar

Yuri Zarhin (Penn State University)

Jordan properties of automorphism groups of complex algebraic varieties abstract

13:15 • EPF Lausanne, Salle MA A3 30

Université de Genève

Séminaire de Topologie et Géométrie

Gaetan Simian (Université de Genève)

Arf invariants of colored links abstract

14:15 • Université de Genève, Conseil Général 7-9, Room 1-15

Université de Genève

Colloque de Mathématiques

Anton Zorich (University Paris Cité)

Random square-tiled surfaces of large genus and random multicurves on surfaces of large genus abstract

16:15 • Université de Genève, Conseil Général 7-9, Room 1-15

ETH Zürich

ITS Science Colloquium

Mihalis Dafermos (Princeton University and University of Cambridge)

The mathematics of black holes and spacetime singularities abstract

16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 3

Universität Basel

Number Theory Web Seminar

Barak Weiss (Tel Aviv University)

New bounds on lattice covering volumes, and nearly uniform covers abstract

17:00 • Universität Basel, online Seminar

ETH Zürich

Talks in Financial and Insurance Mathematics

Dr. Daniel Bartl (Universität Wien)

Statistical estimation of stochastic optimization problems abstract

17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

Friday, May 26

Université de Genève

Lie groups and moduli spaces

Pedram Hekmati (University of Aukland, New Zealand)

Floer theoretic correction terms from finite groups actions abstract

10:30 • Université de Genève, Conseil Général 7-9, Room 1-05

EPF Lausanne

Talks in Mathematical Finance

Eric Loualiche (Carlson School of Management)

Firm networks in the great depression abstract

10:30 • EPF Lausanne, UniL campus, Extranef 126

ETH Zürich

Number Theory Seminar

Prof. Dr. Kevin Hughes (Edinburgh Napier University)

What to do after Vinogradov\'s Mean Value Theorems abstract

14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

ETH Zürich

ZüKoSt Zürcher Kolloquium über Statistik

Tim Vaughan (ETH, Dep. of Biosystems Science and Engineering)

Phylodynamics in Action: Using genomes and computers to understand COVID-19 outbreaks abstract

15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1

EPF Lausanne

Statistics Seminar

Anne van Delft (Columbia University)

CANCELLED: Title T.B.A.

15:15 • EPF Lausanne, Salle GA 3 21

ETH Zürich

Algebraic Geometry and Moduli Seminar

Dr. Michel van Garrel (University of Birmingham)

Geometry of enumerative mirror symmetry abstract

16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

address: Alessandra Naldi Windler, Departement Mathematik, HG G 51.4, ETH Zurich, Raemistrasse 101, CH-8092 Zurich
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