Abstract
The finite element approximation is essentially defined by a mean-square projection of the gradient. Thus, it is natural that error estimates for the gradient of the error directly follow in the L 2 norm. It is interesting to ask whether such a gradient-projection would also be of optimal order in some other norm, for example L. ∞ We prove here that this is the case. Although of interest in their own right, such estimates are also crucial in establishing the viability of approximations of nonlinear problems (Douglas & Dupont 1975) as we indicate in Sect. 7.7. Throughout this chapter, we assume that the domain,Ω ⊂ ℝd is bounded and polyhedral.
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© 1994 Springer Science+Business Media New York
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Brenner, S.C., Scott, L.R. (1994). Max-norm Estimates. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4338-8_8
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DOI: https://doi.org/10.1007/978-1-4757-4338-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-4340-1
Online ISBN: 978-1-4757-4338-8
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