Convergence and optimality of the adaptive Morley element method

Jun Hu; Zhongci Shi; Jinchao Xu

doi:10.1007/s00211-012-0445-0

Convergence and optimality of the adaptive Morley element method

Jun Hu, Zhongci Shi, Jinchao Xu

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

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.

Original language	English (US)
Pages (from-to)	731-752
Number of pages	22
Journal	Numerische Mathematik
Volume	121
Issue number	4
DOIs	https://doi.org/10.1007/s00211-012-0445-0
State	Published - Aug 2012

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1007/s00211-012-0445-0

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title = "Convergence and optimality of the adaptive Morley element method",

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.",

author = "Jun Hu and Zhongci Shi and Jinchao Xu",

note = "Funding Information: 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.",

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N1 - Funding Information: 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.

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N2 - 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.

AB - 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.

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Convergence and optimality of the adaptive Morley element method

Abstract

All Science Journal Classification (ASJC) codes

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