Finite element approximation of the Sobolev constant - Antonietti, Paola; Pratelli, Aldo (Numerische Mathematik, 2011)
Denoting by S the sharp constant in the Sobolev inequality in W(0)(1,2) (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 SE 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.