Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Uniform error estimates for certain narrow Lagrange finite elements

Author: N. Al Shenk
Journal: Math. Comp. 63 (1994), 105-119
MSC: Primary 65N30
MathSciNet review: 1226816
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Error estimates of Dupont and Scott are used to derive uniform error estimates for Lagrange finite elements in $ {\Re ^n}\;(n \geq 2)$ under the following conditions: (1) The elements can be arbitrarily narrow in any coordinate direction such that a sufficient number of interpolation points are grouped on lines parallel to that coordinate axis, and (2) the space of approximating functions $ {F_T}$ in each element T must include the space of polynomials of degree $ \leq m - 1$ for some $ m \geq 1 + n/2$. If n is odd, this does not cover elements of lowest degree that are normally considered with the shape regularity requirement that the ratio of their outer and inner diameters be bounded. For example, if $ n = 3$, the usual requirement with shape regularity is that each $ {F_T}$ contain all first-degree polynomials. The result of this paper requires that each $ {F_T}$ contain all quadratic polynomials, and consequently does not apply to linear (Courant) elements in tetrahedrons or trilinear (tensor) elements in rectangular boxes. Counterexamples in these two cases are included.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30

Retrieve articles in all journals with MSC: 65N30

Additional Information

PII: S 0025-5718(1994)1226816-5
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia