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Article

Kobayashi, Kenta
On the interpolation constants over triangular elements. (English). In: Brandts, J., Korotov, S., Křížek, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Application of Mathematics 2015, In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Proceedings. Prague, November 18-21, 2015. Institute of Mathematics CAS, Prague, 2015. pp. 110-124
MSC: 65D05, 65D30, 65N15 | Zbl 06669923
Keywords:
interpolation error constant; numerical verification method; Finite Element Method
Summary:
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.
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