Published Paper
Inserted: 30 sep 2009
Last Updated: 16 feb 2015
Journal: Numer. Math.
Year: 2010
Abstract:
Denoting by $S$ the sharp constant in the Sobolev inequality in ${\rm W}^{1,2}_0(B)$, being $B$ the unit ball in $R^3$, and denoting by $S_h$ its approximation in a suitable finite element space, we show that $S_h$ converges to $S$ as $h$ goes to $0$ with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results.
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