One World Numerical Analysis

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One World Numerical Analysis

 Nov 29 2021

14:00 - 15:00

Organisers:

  • Lehel Banjai, Heriot-Watt Univerity
  • Emmanuil Georgoulis, University of Leicester/NTU Athens
  • María López Fernández, University of Malaga
  • Charalambos Makridakis, IACM/University of Sussex/Crete
  • Daniel Peterseim, University of Augsburg

 

This is a One World Seminar Series.

The seminars occur every two weeks, on a Monday (14:00-15:00 GMT).

Register Here

Zoom links will be sent on the Friday prior to each seminar, with a reminder on Monday morning.

Recordings of talks given as part of this series can be found here.

 

Future Seminars

 

29 November

Carsten Carstensen (Humboldt-Universität zu Berlin) Half a century of Crouzeix-Raviart finite elements

  • Invented in 1973 for any polynomial degree to solve the Stokes equations with piecewise divergence-free velocities, the    
    Crouzeix-Raviart finite elements allowed various applications to nonlinear PDE over the years. In their lowest-order version,
    they compete  with conforming schemes in elasticity and the Bingham flow. But, most unexpectedly, they allow guaranteed
    lower eigenvalue bounds for the Laplacian and guaranteed lower energy bounds in  convex minimization; they even overcome
    the Lavrentiev phenomenon.

    The presentation discusses contributions to the aforementioned model problems from the speaker's group and former
    students. The circle through all those topics  will be closed with remarks on the very beginning  of the Crouzeix-Raviart
    finite element history: Crouzeix-Raviart   triangular elements are inf-sup stable for any polynomial degree provided the
    mesh has interior vertices. This answers a conjecture of  M. Crouzeix and R. Falk after three decades.

    The time restrictions permit any discussion of  a medius analysis, as addressed e.g. in an overview paper by S. Brenner,  
    or of companion operators. Only minimal comments on the a posteriori error control and  the mathematics of adaptive  
    mesh-refining algorithms might be expected.

    Selected references:

    M. Crouzeix and P. A. Raviart. Conforming and nonconforming finite element methods for solving the stationary
    Stokes equations.  I. Rev. Francaise Automat. Informat. Recherche Operationnelle Ser. Rouge, 7(R-3):33-75, 1973.

    M. Crouzeix and R. Falk. Nonconforming finite elements for Stokes problems.  Math. Comp., 186:437-456, 1989.

    S. Brenner.  Forty years of the Crouzeix-Raviart element.  Numer. Methods Partial Differential Eq 31: 367?396, 2015

    C. Carstensen and S. Sauter: Crouzeix-Raviart triangular elements are inf-sup stable  (2021) arXiv:2105.14987

    C. Carstensen and S. Sauter: Critical Functions and Inf-Sup Stability of Crouzeix-Raviart Elements  (2021) arXiv:2105.14981

 

 

Past Seminars

 

15 November
 
Jesús María Sanz-Serna (University Carlos III of Madrid) Numerical integrators for the Hamiltonian Monte Carlo method
 
 
1 November 2021
 
Ricardo H. Nochetto (U Maryland) Large Isometric Deformations and their LDG Approximation
 
 
18 October 2021
 
Aretha Teckentrup (Edinburgh) - Surrogate models in Bayesian inverse problems
 
 
4 October 2021
 
Ralf Hiptmair (Zurich)  Operator Preconditioning (slides are available here)
 
 
 
24 May 2021

Endre Süli (University of Oxford) - Discrete De Giorgi--Nash--Moser theory and the finite element approximation of chemically reacting fluids
 

3 May 2021

Victorita Dolean (University of Strathclyde, Glasgow) - Robust solvers for time-harmonic wave propagation problems

 

19 April 2021

Andreas Veeser (Università degli Studi di Milano) - Accurate error bounds and equivalence of seminorms

 

22 March 2021

Maria Lopez Fernandez - Pseudospectral Roaming Contour Integral Methods for Convection-Diffusion Equations

 

8 March 2021

Carola-Bibiane Schönlie, University of Cambridge - Structure-Preserving Deep Learning

 

22 February 2021

Wolfgang Dahmen, University of South Carolina - Nonlinear Model Reduction: Recent Developments and Perspectives

 

8 February 2021

Michael Feischl, TU Vienna - Black box Algorithms for Adaptive FEM

 

11 January 2021

Ivan Oseledets, Skolkovo Institute of Science and Technology

 

14 December 2020

Nick Trefethen, University of Oxford - Exactness of Quadrature Formulas

 

30 November 2020

Max Jensen, University of Sussex - Monotone Finite Element Solution of Fully Nonlinear Differential Equations

 

16 November 2020

Desmond Higham, University of Edinburgh - Should We Be Perturbed About Deep Learning?

 

2 November 2020

Houman Owhadi, Caltech - On Learning Adapted Kernels for Numerical Approximation

 

19 October 2020

Virginie Ehrlacher, ENPC - Finite Volume Scheme for the Stefan-Maxwell System

  • Joint work with Clément Cancès and Laurent Monasse
  • Reference: Clément Cancès, Virginie Ehrlacher, Laurent Monasse, Finite volumes for the Stefan-Maxwell cross-diffusion system (2020)

 

5 October 2020

Christian Lubich, University of Tubingen - Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations

 

21 September 2020

Ilaria Perugia, University of Vienna - Space-Time Discontinuous Galerkin Methods for Wave Propagation

 

7 September 2020

Christoph Schwab, ETH Zurich - Exponential Convergence of hp-FEM for Spectral Fractional Diffusion in Polygons

 

20 July 2020

Alfio Quarteroni, Politecnico di Milano/Ecole Polytechnique Fédérale de Lausanne - The Mathematical Heart: a Computational Model for the Simulation of the Heart Function

 

 

This seminar is supported as part of the ICMS Online Mathematical Sciences Seminars.