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?
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asked Jan 30, 2015 at 14:50
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$\begingroup$ After a few days with little feedback, I have crossposted on scicomp.stackexchange. $\endgroup$– Federico PoloniCommented Feb 5, 2015 at 13:05
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$\begingroup$ For what problem? $\endgroup$– usernameCommented Feb 15, 2015 at 20:18
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$\begingroup$ @JungWenChen Any problem -- I am just fishing for idea to apply them to a different setting. $\endgroup$– Federico PoloniCommented Feb 15, 2015 at 21:01
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1 Answer
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This has been solved on scicomp.se (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).
answered Jan 24, 2018 at 23:02