Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Authors
Douglas, J Santos, JE Sheen, D Ye, X
Citation
J. Douglas et al., Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems, RAIRO-M MOD, 33(4), 1999, pp. 747-770
Citations number
13
Categorie Soggetti
Mathematics
Journal title
RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN journal
0764583X → ACNP
Volume
33
Issue
4
Year of publication
1999
Pages
747 - 770
Database
ISI
SICI code
0764-583X(199907/08)33:4<747:NGMBOQ>2.0.ZU;2-3
Abstract
Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary condi tions. Both simplicial and rectangular elements will be considered in two a nd three dimensions. The simplicial elements will be based On P-1, as for c onforming elements; however, it is necessary to introduce new elements in t he rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H-1(Omega) and in the Neumann and Ro bin cases in L-2(Omega).