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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

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Volume 15, Issue 3


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
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/ Jun Hu
Published Online: 2015-06-13 | DOI: https://doi.org/10.1515/cmam-2015-0017


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.

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