Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-05-01

Journal: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Included Journals: Scopus、EI、SCIE

Volume: 31

Issue: 3

Page Number: 691-705

ISSN: 0749-159X

Key Words: nonconforming finite element; optimal error estimates; quadrilateral mesh

Abstract: A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the 12 values at the three Gauss points on each of the four edges. Due to the existence of one linear relation among the above DOFs, it turns out the DOFs are 11. The nonconforming element consists of . We count the corresponding dimension for Dirichlet and Neumann boundary value problems of second-order elliptic problems. We also present the optimal error estimates in both broken energy and norms. Finally, numerical examples match our theoretical results very well. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 691-705, 2015