Numerische Mathematik

, Volume 121, Issue 4, pp 731–752

Convergence and optimality of the adaptive Morley element method

Article

DOI: 10.1007/s00211-012-0445-0

Cite this article as:
Hu, J., Shi, Z. & Xu, J. Numer. Math. (2012) 121: 731. doi:10.1007/s00211-012-0445-0

Abstract

This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method. By introducing a new parameter-dependent error estimator and further establishing a discrete reliability property, sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem.

Mathematics Subject Classification (2010)

65N30 65N15 35J30 

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.LMAM and School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China
  2. 2.Institute of Computational MathematicsChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.The School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China
  4. 4.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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