Generalized Park-Sheen Finite Elements for Adaptivity

The P1-nonconforming finite element method on simply connected Lipschitz domains partitioned into quadrilaterals was introduced by Park and Sheen in 2003. In order to apply mesh-adaptive refinement strategies, the concept is generalized to arbitrary triangulations into quadrilaterals and triangles of multiple connected Lipschitz domains. An explicit a priori analysis is given for second-order elliptic PDEs with inhomogeneous Dirichlet boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)