Crouzeix–Raviart boundary elements

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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 Poincare–Friedrichs inequality in fractional order Sobolev spaces. A numerical experiment confirms the predicted convergence of Crouzeix–Raviart boundary elements.