10.18452/2566
Carstensen, Carsten
Hu, Jun
Orlando, Antonio
Framework For The A Posteriori Error Analysis Of Nonconforming Finite Elements
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
2005
Finite elements
Rayleigh-Ritz and Galerkin methods
finite methods
Error bounds
510 Mathematik
Humboldt-Universität zu Berlin
Humboldt-Universität zu Berlin
2017-06-15
2017-06-15
2005-11-02
2005-04-08
0863-0976
http://edoc.hu-berlin.de/18452/3218
urn:nbn:de:kobv:11-10051862
This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions $(H1)-(H2)$ and applies to several nonconforming finite elements: the Crouzeix-Raviart triangle element, the Han parallelogram element, the nonconforming rotated (NR) parallelogram element of Rannacher and Turek, the constrained NR parallelogram element of Hu and Shi, the $P_1$ element on parallelograms due to Park and Sheen, and the DSSY parallelogram element.