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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 7, Pages 1178–1191 (Mi zvmmf9830)  

This article is cited in 1 scientific paper (total in 1 paper)

Application of functional error estimates with mixed approximations to plane problems of linear elasticity

M. E. Frolov

Saint-Petersburg State Polytechnical University

Abstract: S. I. Repin and his colleagues' studies addressing functional a posteriori error estimates for solutions of linear elasticity problems are further developed. Although the numerical results obtained for planar problems by A. V. Muzalevsky and Repin point to advantages of the adaptive approach used, the degree of overestimation of the absolute error increases noticeably with mesh refinement. This shortcoming is eliminated by using approximations typical of mixed finite element methods. A comparative analysis is conducted for the classical finite element approximations, mixed Raviart–Thomas approximations, and relatively recently proposed Arnold–Boffi–Falk mixed approximations. It is shown that the last approximations are the most efficient.

Key words: functional a posteriori estimates, elasticity problems, plane strain, mixed approximations, finite element method.

DOI: https://doi.org/10.7868/S0044466913070090

Full text: PDF file (571 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:7, 1000–1012

Bibliographic databases:

UDC: 519.634
Received: 24.12.2012
Revised: 14.02.2013

Citation: M. E. Frolov, “Application of functional error estimates with mixed approximations to plane problems of linear elasticity”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1178–1191; Comput. Math. Math. Phys., 53:7 (2013), 1000–1012

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Frolov M.Y., “Functional a Posteriori Estimates of the Error in the Solutions of Plane Problems in Cosserat Elasticity Theory”, Pmm-J. Appl. Math. Mech., 78:4 (2014), 425–431  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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