Finite element approximation of the Sobolev constant
نویسندگان
چکیده
Denoting by S the sharp constant in the Sobolev inequality in W 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 ↘ 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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ورودعنوان ژورنال:
- Numerische Mathematik
دوره 117 شماره
صفحات -
تاریخ انتشار 2011