Kiel Nano, Surface and Interface Science (KiNSIS)

A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions (Prof. Sauter, Zürich)

21.07.2017 von 14:15 bis 15:45

Institut für Informatik, Ludewig-Meyn-Straße 2, 24118 Kiel, Raum: Übungsraum 2/K

Abstract:

In this talk we will present a family of non-conforming "Crouzeix-Raviart" type finite elements in two and three dimensions. They consist of local polynomials of maximal degree p on simplicial finite element meshes while certain jump conditions are imposed across adjacent simplices.

We will prove optimal a priori estimates for these finite elements. The characterization of this space via jump conditions goes back to the seminal paper of Crouzeix and Raviart in 1973. However, the definition is implicit and the derivation of an explicit representation of the local basis functions for general p in 3D was an open problem.

We present explicit representations for these functions by developing some theoretical tools for fully symmetric and reflection symmetric orthogonal polynomials on triangles and their representation.

Finally we will analyze the linear independence of these sets of functions and discuss the question whether they span the whole non-conforming space. This talk comprises joint work with P. Ciarlet Jr., ENSTA, Paris and Charles F. Dunkl, Virginia Tech.

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