Numerische Mathematik

, Volume 121, Issue 4, pp 731–752

Convergence and optimality of the adaptive Morley element method

Authors

    • LMAM and School of Mathematical SciencesPeking University
  • Zhongci Shi
    • Institute of Computational MathematicsChinese Academy of Sciences
  • Jinchao Xu
    • The School of Mathematical SciencesPeking University
    • Department of MathematicsPennsylvania State University
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)

65N3065N1535J30

Copyright information

© Springer-Verlag 2012