We will now develop the approximation theory appropriate for the finite elements developed in Chapter 3. We take a constructive approach, defining an averaged version of the Taylor polynomial familiar from calculus. The key estimates are provided by some simple lemmas from the theory of Riesz potentials, which we derive. As a corollary, we provide a proof of Sobolev's inequality, much in the spirit given originally by Sobolev.
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© 2008 Springer Science+Business Media, LLC
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(2008). Polynomial Approximation Theory in Sobolev Spaces. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75934-0_5
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DOI: https://doi.org/10.1007/978-0-387-75934-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-75933-3
Online ISBN: 978-0-387-75934-0
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