Two-sided bounds for eigenvalues of differential operators with applications to Friedrichs', Poincar\'e, trace, and similar constants
| Autor: | Šebestová, Ivana, Vejchodský, Tomáš |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | SIAM J. Numer. Anal. 52-1 (2014), pp. 308-329 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1137/13091467X |
| Popis: | We present a general numerical method for computing guaranteed two-sided bounds for principal eigenvalues of symmetric linear elliptic differential operators. The approach is based on the Galerkin method, on the method of a priori-a posteriori inequalities, and on a complementarity technique. The two-sided bounds are formulated in a general Hilbert space setting and as a byproduct we prove an abstract inequality of Friedrichs'-Poincar\'e type. The abstract results are then applied to Friedrichs', Poincar\'e, and trace inequalities and fully computable two-sided bounds on the optimal constants in these inequalities are obtained. Accuracy of the method is illustrated on numerical examples. Comment: Extended numerical experiments and minor corrections of the previous version. This version has been accepted for publication by SIAM J. Numer. Anal |
| Databáze: | arXiv |
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