Computing upper bounds on Friedrichs' constant

0376943 - MÚ 2013 RIV CZ eng C - Conference Paper (international conference)
Vejchodský, Tomáš
Computing upper bounds on Friedrichs' constant.
Proceedings of the International Conference Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012 - (Brandts, J.; Chleboun, J.; Korotov, S.; Segeth, K.; Šístek, J.; Vejchodský, T.), s. 278-289. ISBN 978-80-85823-60-8.
[Applications of Mathematics 2012. Prague (CZ), 02.05.2012-05.05.2012]
R&D Projects: GA AV ČR IAA100760702
Institutional support: RVO:67985840
Keywords : Friedrichs' constant
Subject RIV: BA - General Mathematics
http://www.math.cas.cz/~am2012/proceedings/contributions/vejchodsky.pdf

This contribution shows how to compute upper bounds of the optimal constant in Friedrichs’ and similar inequalities. The approach is based on the method of a prioria posteriori inequalities [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs’ constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed upper bound on Friedrichs’ constant in a posteriori error estimation to obtain guaranteed error bounds.
Permanent Link: http://hdl.handle.net/11104/0209222