Graduate School of Mathematical Sciences, University of Tokyo
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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
17
号
1
ページ
27 - 78
発行年
2010-07-20
ISSN
13405705
書誌レコードID
AA11021653
日本十進分類法
415
Mathematical Reviews Number
MR
Mathmatical Subject Classification
65N15(MSC2000)
65N30(MSC2000)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2008-07-22
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Analysis and Estimation of Error Constants for P0 and P1 Interpolations over Triangular Finite Elements
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