High-order non-conforming finite elements for the Stokes equation

Overview

Abstract

We consider non-conforming discretizations of the stationary Stokes equation in two and three dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice.
In our talk, we introduce canonical Crouzeix-Raviart basis functions in 2D and 3D in a fully explicit way. We prove that results on the well-posedness of canonical Crouzeix-Raviart element for the Stokes equation. We identify spurious pressure modes for the conforming (k,k-1) 3D Stokes element and show that these are eliminated by using the canonical Crouzeix-Raviart space

Brief Biography

Stefan Sauter (born in Heidelberg) is a German-swiss mathematician, whose field of research is numerical analysis.

He studied mathematics and physics at the University of Heidelberg (1985-1990) and moved to the University of Kiel for his Ph.D. (1990-1993). The title of his thesis is "On the efficient use of the Galerkin method for solving Fredholm integral equations". 
During 1993/94 he was a post-doc at the University of Maryland, College Park and, afterward, went back to Kiel for his habiliation (1998); title: Coarsening of finite element spaces.

In 1998 he became a full professor at the University of Leipzig and moved to the University of Zurich (1999) for a chair in applied mathematics. His main research interest is the development of fast numerical methods for solving integral and differential equations. He is the (co)author of three monographs and more than 100 peer-reviewed journal publications. 1996 he was awarded the Oberwolfach-price. Since 2020 he is a member of the European Academy of Sciences.