Franz Chouly: Thursday 15 February at 2 pm, A415 Inria Paris.
In the first part of this talk, we will present a residual based a posteriori error estimate for contact problems in small strain elasticity, discretized with finite elements and Nitsche’s method. Upper and lower bounds are established under a saturation assumption. This theoretical results will be illustrated by some numerical experiments (joint work with Mathieu Fabre, Patrick Hild, Jérôme Pousin and Yves Renard).
In the second part of this talk, we will present preliminary results on goal oriented error estimates for soft-tissue biomechanics, still under small strain assumptions. The performance of the Dual Weighted Residual method will be assessed for two simplified scenarios involving tongue muscular activation, and contraction of the arterial wall. Open mathematical questions and the potential interest of such a methodology for computational biomechanics will be discussed (joint work with Stéphane Bordas, Marek Bucki, Michel Duprez, Vanessa Lleras, Claudio Lobos, Alexei Lozinski, Pierre-Yves Rohan and Satyendra Tomar).