On the interpolation constants over triangular elements

Kobayashi, Kenta

  • Application of Mathematics 2015, Publisher: Institute of Mathematics CAS(Prague), page 110-124

Abstract

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We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants are obtained via the numerical verification method. Furthermore, we introduce remarkable formulas for the upper bounds of these constants.

How to cite

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Kobayashi, Kenta. "On the interpolation constants over triangular elements." Application of Mathematics 2015. Prague: Institute of Mathematics CAS, 2015. 110-124. <http://eudml.org/doc/287821>.

@inProceedings{Kobayashi2015,
abstract = {We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants are obtained via the numerical verification method. Furthermore, we introduce remarkable formulas for the upper bounds of these constants.},
author = {Kobayashi, Kenta},
booktitle = {Application of Mathematics 2015},
keywords = {interpolation error constant; numerical verification method; Finite Element Method},
location = {Prague},
pages = {110-124},
publisher = {Institute of Mathematics CAS},
title = {On the interpolation constants over triangular elements},
url = {http://eudml.org/doc/287821},
year = {2015},
}

TY - CLSWK
AU - Kobayashi, Kenta
TI - On the interpolation constants over triangular elements
T2 - Application of Mathematics 2015
PY - 2015
CY - Prague
PB - Institute of Mathematics CAS
SP - 110
EP - 124
AB - We propose a simple method to obtain sharp upper bounds for the interpolation error constants over the given triangular elements. These constants are important for analysis of interpolation error and especially for the error analysis in the Finite Element Method. In our method, interpolation constants are bounded by the product of the solution of corresponding finite dimensional eigenvalue problems and constant which is slightly larger than one. Guaranteed upper bounds for these constants are obtained via the numerical verification method. Furthermore, we introduce remarkable formulas for the upper bounds of these constants.
KW - interpolation error constant; numerical verification method; Finite Element Method
UR - http://eudml.org/doc/287821
ER -

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