, Volume 121, Issue 4, pp 731-752
Date: 03 Feb 2012

Convergence and optimality of the adaptive Morley element method

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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.

The first author was supported in part by the NSFC Key Project 11031006 under Grant 10971005, and Foundation for the Author of National Excellent Doctoral Dissertation of PR China 200718, and partially supported by the Chinesisch-Deutsches Zentrum project GZ578. The third author was supported in part by NSF 0915153 and NSFC-10528102.