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.
@article{702969,
title = {On the interpolation constants over triangular elements},
booktitle = {Application of Mathematics 2015},
series = {GDML\_Books},
publisher = {Institute of Mathematics CAS},
address = {Prague},
year = {2015},
pages = {110-124},
zbl = {06669923},
url = {http://dml.mathdoc.fr/item/702969}
}
Kobayashi, Kenta. On the interpolation constants over triangular elements, dans Application of Mathematics 2015, GDML_Books, (2015), pp. 110-124. http://gdmltest.u-ga.fr/item/702969/