Approximation classes for adaptive higher order finite element approximation

Gaspoz, Fernando; Morin, Pedro

doi:10.1090/S0025-5718-2013-02777-9

Approximation classes for adaptive higher order finite element approximation
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by Fernando D. Gaspoz and Pedro Morin PDF

Math. Comp. 83 (2014), 2127-2160 Request permission

Erratum: Math. Comp. 86 (2017), 1525-1526.

Abstract:

We provide an almost characterization of the approximation classes appearing when using adaptive finite elements of Lagrange type of any fixed polynomial degree. The characterization is stated in terms of Besov regularity, and requires the approximation within spaces with integrability indices below one. This article generalizes to higher order finite elements the results presented for linear finite elements by Binev et. al.

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