A robust nonconforming H-2-element

• Main Authors: Nilssen, Trygve K., Tai, Xue Cheng, Winther, Ragnar
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
• Online Access: https://hdl.handle.net/10356/91499; http://hdl.handle.net/10220/6056; http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2001&volume=70&issue=234&spage=489&epage=505&aulast=Nilssen&aufirst=%20T%20K&auinit=&title=Mathematics%20of%20Computation&atitle=A%20robust%20nonconforming%20H.
• Institution: Nanyang Technological University

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming H-2-element which is H-1-conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter.