This contribution presents a general numerical method for computing lower and upper bound of the optimal constant in Friedrichs’ inequality. The standard Rayleigh-Ritz method is used for the lower bound and the method of $𝑎\mathrm{𝑝𝑟𝑖𝑜𝑟𝑖}-𝑎\mathrm{𝑝𝑜𝑠𝑡𝑒𝑟𝑖𝑜𝑟𝑖}\mathrm{𝑖𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑖𝑒𝑠}$ is employed for the upper bound. Several numerical experiments show applicability and accuracy of this approach.

EUDML-ID : urn:eudml:doc:271391
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@article{702727,
     title = {Guaranteed and fully computable two-sided bounds of Friedrichs' constant},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {195-201},
     url = {http://dml.mathdoc.fr/item/702727}
}

Vejchodský, Tomáš. Guaranteed and fully computable two-sided bounds of Friedrichs’ constant, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2013), pp. 195-201. http://gdmltest.u-ga.fr/item/702727/