NDLI: P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Park, Chunjae Sheen, Dongwoo
Copyright Year	2003
Abstract	A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom among the nonconforming quadrilateral elements. An optimal rate of convergence is obtained. Also a nonparametric reference scheme is introduced in order to systematically compute stiffness and mass matrices on each quadrilateral. An extension of the P1 -nonconforming element to three dimensions is also given. Finally, several numerical results are reported to confirm the effective nature of the proposed new element.
Starting Page	624
Ending Page	640
Page Count	17
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142902404923
e-ISSN	10957170
Issue Number	2
Volume Number	41
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods nonconforming finite elements quadrilateral elliptic problems Error bounds Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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