Approximation classes for adaptive higher order finite element approximation

GASPOZ, FERNANDO; MORIN, PEDRO

MATHEMATICS OF COMPUTATION

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2012

0025-5718

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 nite elements the results presented for linear nite elements by Binev et. al. in Binev-Dahmen-DeVore-Petrushev, Approximation Classes for Adaptive Methods, Serdica Math. J. 28 (2002), pp. 391--416