Bienvenue - Laboratoire Jacques-Louis Lions

Annalisa Buffa (Ecole Polytechnique Fédérale de Lausanne)
Leçons Jacques-Louis Lions 2018 - Colloquium
New trends in finite element theory : the isogeometric method

Le colloquium des Leçons Jacques-Louis Lions 2018 aura lieu
salle du séminaire du Laboratoire Jacques-Louis Lions,
barre 15-16, 3ème étage, salle 09 (15-16-309),
Sorbonne Université, Campus Jussieu, 4 place Jussieu, Paris 5ème

Résumé du colloquium
New trends in finite element theory : the isogeometric method
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.