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P1-Nonconforming finite elements on triangulations into triangles and quadrilaterals

Altmann, Robert; Carstensen, C.

The P1-nonconforming finite element is introduced for arbitrary triangulations into quadrilaterals and triangles of multiple connected Lipschitz domains. An explicit a priori analysis for the combination of the Park–Sheen and the Crouzeix–Raviart nonconforming finite element methods is given for second-order elliptic PDEs with inhomogeneous Dirichlet boundary conditions.
Published in: SIAM journal on numerical analysis, 10.1137/110823675, Society for Industrial and Applied Mathematics