  We consider the finite element approximation of fractional powers of
regularly accretive operators via the Dunford-Taylor integral approach. We use
a sinc quadrature scheme to approximate the Balakrishnan representation of the
negative powers of the operator as well as its finite element approximation. We
improve the exponentially convergent error estimates from [A. Bonito, J. E.
Pasciak, IMA J. Numer. Anal. (2016) 00, 1-29] by reducing the regularity
required on the data. Numerical experiments illustrating the new theory are
provided.
