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タイトル: Analysis and Estimation of Error Constants for P0 and P1 Interpolations over Triangular Finite Elements
著者: Liu, Xuefeng
Kikuchi, Fumio
キーワード: FEM
error estimates
triangular finite elements
interpolation error constants
発行日: 2010年7月20日
出版者: Graduate School of Mathematical Sciences, The University of Tokyo
掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 17 (2010), No. 1, Page 27-78
抄録: We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but the present results also appear to be available for the non-conforming case. We obtain explicit relations for the upper bounds of the constants, and analyze dependence of such constants on the geometric parameters of triangles. In particular, we explicitly determine some special constants including the Babuška-Aziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element. The obtained results are expected to be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of numerical solutions based on the triangular finite elements. We also give some numerical results for the error constants and for a posteriori estimates of some eigenvalues related to the error constants.
URI: http://hdl.handle.net/2261/52393
ISSN: 13405705
出現カテゴリ:Journal of Mathematical Sciences, the University of Tokyo
Journal of Mathematical Sciences, the University of Tokyo

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