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Applications of discrete maximal L p regularity for finite element operators

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Abstract

In this paper, we present applications of discrete maximal L p regularity for finite element operators. More precisely, we show error estimates of order h 2 for linear and certain semilinear problems in various L p (Ω)-norms. Discrete maximal regularity allows us to prove error estimates in a very easy and efficient way. Moreover, we also develop interpolation theory for (fractional powers of) finite element operators and extend the results on discrete maximal L p regularity formerly proved by the author.

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Correspondence to Matthias Geissert.

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The author was supported by the DFG-Graduiertenkolleg 853.

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Geissert, M. Applications of discrete maximal L p regularity for finite element operators. Numer. Math. 108, 121–149 (2007). https://doi.org/10.1007/s00211-007-0110-1

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  • DOI: https://doi.org/10.1007/s00211-007-0110-1

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