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Title: Local finite element approximation of Sobolev differential forms
We address fundamental aspects in the approximation theory of vector-valued finite element methods, using finite element exterior calculus as a unifying framework. We generalize the Clément interpolant and the Scott-Zhang interpolant to finite element differential forms, and we derive a broken Bramble-Hilbert lemma. Our interpolants require only minimal smoothness assumptions and respect partial boundary conditions. This permits us to state local error estimates in terms of the mesh size. Our theoretical results apply to curl-conforming and divergence-conforming finite element methods over simplicial triangulations.  more » « less
Award ID(s):
2012427 2012857
NSF-PAR ID:
10327856
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
ESAIM: Mathematical Modelling and Numerical Analysis
Volume:
55
Issue:
5
ISSN:
0764-583X
Page Range / eLocation ID:
2075 to 2099
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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