Denoting by S the sharp constant in the Sobolev inequality in W1,2 0 (B), being B the unit ball in ℝ, and denoting by Sh its approximation in a suitable finite element space, we show that Sh converges to S as h {south east double arrow} 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.

Finite Element Approximation of Sobolev Constant

PRATELLI, ALDO
2011-01-01

Abstract

Denoting by S the sharp constant in the Sobolev inequality in W1,2 0 (B), being B the unit ball in ℝ, and denoting by Sh its approximation in a suitable finite element space, we show that Sh converges to S as h {south east double arrow} 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/224689
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