Bienvenue - Laboratoire Jacques-Louis Lions

Annalisa Buffa (Ecole Polytechnique Fédérale de Lausanne)

New trends in finite element theory : the isogeometric method

Cette séance du séminaire s’inscrira dans le cadre des Leçons Jacques-Louis Lions 2018
https://www.ljll.math.upmc.fr/lecons-jacques-louis-lions-2018-annalisa-buffa
Les Leçons Jacques-Louis Lions 2018 comprendront également un mini-cours
The interplay of geometric modelling and numerical analysis of PDEs
qui sera donné par Annalisa Buffa les mercredi 21, jeudi 22 et vendredi 23 novembre 2018 de 11h00 à 12h30.

Résumé
Numerical methods for partial differential equations (PDEs) is a branch of numerical analysis which offers scientific challenges spanning from functional analysis to computer science and code design. The discretisation of differential problems beyond the elliptic case and in the non linear context often requires special choices of discretisation spaces, and robust discretisations are the result of a deep understanding of the mathematical structures of the problem to solve.
In the last ten years the use of splines as a tool for the discretisation of partial differential equations has gained interest thanks to the advent of isogeometric analysis. For this class of methods, all robust and accurate techniques aiming at enhancing the flexibility of splines, while keeping their structure, are of paramount importance since the tensor product structure underlying spline constructions is far too restrictive in the context of approximation of partial differential equations.
I will describe various approaches, from adaptivity with regular splines to patch gluing and to trimming. Moreover, I will show applications and test benches in (non linear) mechanics, such as large deformation problems with contact and quasi-incompressible materials.