The global-best H(div) approximation error with divergence and boundary constraints is equivalent, up to a generic constant, to the sum of unconstrained local-best errors, yielding a local commuting projector and hp-optimal error estimates under minimal regularity.
Quelques propri´ et´ es d’approximation des ´ el´ ements finis de N´ed´ elec, application ` a l’analyse a posteriori
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Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal $hp$ approximation estimates in $H(\mathrm{div})$
The global-best H(div) approximation error with divergence and boundary constraints is equivalent, up to a generic constant, to the sum of unconstrained local-best errors, yielding a local commuting projector and hp-optimal error estimates under minimal regularity.