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)


A counterexample concerning the $ L_2$-projector onto linear spline spaces

Author: Peter Oswald
Journal: Math. Comp. 77 (2008), 221-226
MSC (2000): Primary 65N30, 41A15
Published electronically: September 13, 2007
MathSciNet review: 2353950
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For the $ L_2$-orthogonal projection $ P_V$ onto spaces of linear splines over simplicial partitions in polyhedral domains in $ \mathbb{R}^d$, $ d>1$, we show that in contrast to the one-dimensional case, where $ \Vert P_V\Vert _{L_\infty\to L_\infty} \le 3$ independently of the nature of the partition, in higher dimensions the $ L_\infty$-norm of $ P_V$ cannot be bounded uniformly with respect to the partition. This fact is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65N30, 41A15

Retrieve articles in all journals with MSC (2000): 65N30, 41A15

Additional Information

Peter Oswald
Affiliation: School of Engineering and Science, Jacobs University, D-28759 Bremen, Germany

PII: S 0025-5718(07)02059-5
Received by editor(s): December 20, 2006
Published electronically: September 13, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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