Publication at Faculty of Mathematics and Physics |
2020
Abstract
This paper gives a direct proof of localization of dual norms of bounded linear functionals on the Sobolev space W-0(1,p) (Omega), 1 <= p <= infinity. The basic condition is that the functional in question vanishes over locally supported test functions from W-0(1,p) (Omega) which form a partition of unity in O, apart from close to the boundary partial derivative Omega.
We also study how to weaken this condition. The results allow in particular to establish local efficiency and robustness with respect to the exponent p of a posteriori estimates for nonlinear partial differential equations in divergence form, including the case of inexact solvers.
Numerical illustrations support the theory.