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Generalized Park‐Sheen Finite Elements for Adaptivity
Author(s) -
Altmann Robert,
Carstensen Carsten
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210318
Subject(s) - quadrilateral , finite element method , lipschitz continuity , a priori and a posteriori , order (exchange) , mathematics , boundary (topology) , dirichlet distribution , pure mathematics , boundary value problem , mathematical analysis , structural engineering , engineering , economics , philosophy , epistemology , finance
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)