## Virtual Seminar Series - One World Numerical Analysis Series

This is the webpage for the One World Numerical Analysis Series. The seminars every two weeks, on a Monday (14:00-15:00 GMT).

The first seminar will be held on 20th July followed by a break until September at which point the series will resume.

Organisers are Lehel Banjai (Heriot-Watt Univerity), Emmanuil Georgoulis (University of Leicester/NTU Athens), Charalambos Makridakis (IACM/University of Sussex/Crete) and Daniel Peterseim (University of Augsburg).

**To sign up for this seminar series, please complete this form.**

Zoom links will be sent at 11:00 GMT on the day of each seminar

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

### Future Seminars

30 November

Max Jensen(University of Sussex)Title:

Monotone Finite Element Solution of Fully Nonlinear Differential Equations

Fully nonlinear partial differential equations arise naturally in optimal control, game theory, optimal transport, differential geometry and resulting applications. PDE solutions often lack regularity and their uniqueness is delicate. Indeed, weak solutions are usually not unique and alternative concepts such as that of viscosity solutions are needed. This talk addresses the finite element approximation in such settings, focussing on Hamilton-Jacobi-Bellman equations of optimal control, and Monge-Ampère equations related to optimal transport. Attention will be on the following questions:How can fully nonlinear BVPs with mixed and nonlinear boundary conditions be approximated?

How can convexity be imposed discretely while maintaining access to a comparison principle?

How can convergence in norms stronger than be guaranteed, even when the PDE degenerates?The talk is based on joint work with B. Jaroszkowski, X. Feng and I. Smears.

14 December

Nick Trefethen(University of Oxford)Title: Exactness of Quadrature Formulas

Quadrature is a problem of analysis, but the standard design principle for quadrature formulas is an algebraic one: exactness when applied to a specified set of functions. The result is

that quadrature formulas may converge more slowly, or faster, than one might naturally expect. We discuss five examples: (1) Newton-Cotes, (2) Clenshaw-Curtis, (3) Interpolatory formulas,(4) Cubature in the hypercube, and (5) Hermite and Laguerre.

### Previous Seminars

16 November

Desmond Higham(University of Edinburgh)Title:

Should We Be Perturbed About Deep Learning?

02 November

Houman Owhadi(Caltech)Title:

On learning adapted kernels for numerical approximationAbstract: Most numerical approximation methods can be interpreted as kernel interpolation methods. The particular choice of the kernel can have a large impact on the accuracy/complexity of the method and this talk is an invitation to explore the problem of selecting/learning the underlying kernel.

Slides are available here.

19 October

Virginie Ehrlacher(CERMICS - ENPC)Title:

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)

05 October

Christian Lubich(University of Tubingen)Title:

Convergent evolving surface finite element algorithms for geometric evolution equationsLecture notes can be found here.

21 September

Ilaria Perugia(Vienna)

Space-time discontinuous Galerkin methods for wave propagationSlides for talk are here

07 September

Christoph Schwab(SAM, ETH Zurich)

Exponential Convergence of hp-FEM for Spectral Fractional Diffusion in PolygonsSlides for talk are here

20 July

Alfio Quarteroni(Politecnico di Milano/Ecole Polytechnique Fédérale de Lausanne (EPFL))

The mathematical heart: a computational model for the simulation of the heart function

This is a One World Seminar Series.

Zoom is the online platform being used to deliver this seminar series

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