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.File in questo prodotto:
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