Foundations of Computational Mathematics

, Volume 16, Issue 1, pp 33–68 | Cite as

Instance Optimality of the Adaptive Maximum Strategy

Article

Abstract

In this paper, we prove that the standard adaptive finite element method with a (modified) maximum marking strategy is instance optimal for the total error, being the square root of the squared energy error plus the squared oscillation. This result will be derived in the model setting of Poisson’s equation on a polygon, linear finite elements, and conforming triangulations created by newest vertex bisection.

Keywords

Adaptive finite element method Maximum marking Instance optimality Newest vertex bisection 

Mathematics Subject Classification

41A25 65N12 65N30 65N50 

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Copyright information

© SFoCM 2014

Authors and Affiliations

  • Lars Diening
    • 1
  • Christian Kreuzer
    • 2
  • Rob Stevenson
    • 3
  1. 1.Mathematisches Institut der Universität MünchenMünichGermany
  2. 2.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  3. 3.Korteweg-de Vries Institute (KdVI) for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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