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Article

Vejchodský, Tomáš
Computing upper bounds on Friedrichs’ constant. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 278-289
MSC: 35A23, 35J25, 65N15, 65N30 | MR 3204419 | Zbl 1313.65296
Keywords:
second-order boundary value problems; a posteriori error estimates; complementary energy; Friedrichs’ inequality; numerical example
Summary:
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 $a priori-a posteriori inequalities$ [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.
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