Back to Events of Week No. 2: Monday 08th January 2018 to Sunday 14th January 2018
Wednesday | 04:15 PM | Stabilised Finite Element Methods for Variational Inequalities IWR Colloquium Prof. Rolf Stenberg, Aalto University, Finland We survey our recent and ongoing work [1,2] on finite element methods for contact problems. Our approach is to first write the problem in mixed form, in which the contact pressure act as a Lagrange multiplier. In order to avoid the problems related to a direct mixed finite element discretisation, we use a stabilised formulation, in which appropriately weighted residual terms are added to the discrete variational forms. We prove that the formulation is uniformly stable, which implies an optimal a priori error estimate. Using the stability of the continuous problem, we also prove a posteriori estimates, the optimality of which is ensured by local lower bounds. In the implementation of the methods, the discrete Lagrange multiplier is locally eliminated, leading to a Nitsche-type method [3]. Address Mathematikon Conference Room / 5th Floor Im Neuenheimer Feld 205 69120 Heidelberg Homepage Event www.iwr.uni-heidelberg.de/iwr-colloquium Organizer Interdisciplinary Center for Scientific Computing (IWR) Homepage Organizer Contact |