Crouzeix-Raviart boundary elements
Norbert Heuer and Francisco-Javier Sayas
Numer. Math. 112 (3), 381-401, 2009.
This paper establishes a foundation of non-conforming boundary elements.
We present a discrete weak formulation of hypersingular integral operator
equations that uses Crouzeix-Raviart elements for the approximation.
The cases of closed and open polyhedral surfaces are dealt with.
We prove that, for shape regular elements, this non-conforming boundary
element method converges and that the usual convergence rates of
conforming elements are achieved.
Key ingredient of the analysis is a discrete Poincaré-Friedrichs
inequality in fractional order Sobolev spaces.
A numerical experiment confirms the predicted convergence of Crouzeix-Raviart
boundary elements.