2024-03-28T15:02:22Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00040064
2022-12-19T04:14:59Z
312:6865:6919:6927
9:504:6868:6921:6928
Analysis and Estimation of Error Constants for P0 and P1 Interpolations over Triangular Finite Elements
Liu, Xuefeng
92522
Kikuchi, Fumio
92523
415
FEM
error estimates
triangular finite elements
interpolation error constants
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.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
2010-07-20
application/pdf
Journal of mathematical sciences, the University of Tokyo
1
17
27
78
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40064/files/jms170102.pdf
eng