Section: New Results

Localization of dual and distance norms

Participants : Martin Vohralík, Patrick Ciarlet Jr., Jan Blechta, Josef Málek.

Dual norms like the dual norm of the residual and the distance norm to the Sobolev space $H_0^1$ seem to be fundamentally global over the entire computational domain. In [23], together with P. Ciarlet, we prove, in extension of some older results, that they are both equivalent to the Hilbertian sums of their localizations over patches of elements. Together with J. Blechta and J. Málek, we extend in [45] this result from the space $H_0^1$ with Hilbertian structure to the Sobolev space $W_0^{1,p}$, with the exponent $p$ bigger than or equal to one, and to an arbitrary bounded linear functional on $W_0^{1,p}$.