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).
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
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.