Are there finite element method setups that provide error estimates in the $W^{1,\infty}$ norm (i.e., bounds on $\|u'\_h - u'\|\_\infty$)? Which families of elements can be used for implementing them?



Finite elements $W^{1,\infty}$ error estimates
This has been solved on [scicomp.se](https://scicomp.stackexchange.com/questions/18852/finite-elements-w1-infty-error-estimates) (TL;DR: Chapter 8 of Brenner and Scott's Mathematical Theory of Finite Element Methods, $\|u - u\_h\|\_{W^1\_\infty} \le C h^{k - 1}\|u\|\_{W^k\_\infty}$).


(I'm posting this to prevent this question from being bumped up because it has no answers).


