Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

Online
ISSN
1609-9389
See all formats and pricing
More options …
Volume 15, Issue 3

Issues

An Optimal Adaptive Finite Element Method for an Obstacle Problem

Carsten Carstensen
  • Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; and Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jun Hu
Published Online: 2015-06-13 | DOI: https://doi.org/10.1515/cmam-2015-0017

Abstract

This paper provides a refined a posteriori error control for the obstacle problem with an affine obstacle which allows for a proof of optimal complexity of an adaptive algorithm. This is the first adaptive mesh-refining finite element method known to be of optimal complexity for some variational inequality. The result holds for first-order conforming finite element methods in any spacial dimension based on shape-regular triangulation into simplices for an affine obstacle. The key contribution is the discrete reliability of the a posteriori error estimator from [Numer. Math. 107 (2007), 455–471] in an edge-oriented modification which circumvents the difficulties caused by the non-existence of a positive second-order approximation [Math. Comp. 71 (2002), 1405–1419].

About the article

Received: 2015-05-01

Revised: 2015-05-25

Accepted: 2015-05-27

Published Online: 2015-06-13

Published in Print: 2015-07-01


Funding Source: DFG Research Center MATHEON

Funding Source: WCU program through KOSEF

Award identifier / Grant number: R31-2008-000-10049-0

Funding Source: NSFC

Award identifier / Grant number: 11271035, 91430213, 11421101


Citation Information: Computational Methods in Applied Mathematics, Volume 15, Issue 3, Pages 259–277, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0017.

Export Citation

© 2015 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
[2]
Susanne C. Brenner, Joscha Gedicke, Li-Yeng Sung, and Yi Zhang
SIAM Journal on Numerical Analysis, 2017, Volume 55, Number 1, Page 87

Comments (0)

Please log in or register to comment.
Log in