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On sinc quadrature approximations of fractional powers of regularly accretive operators

  • Andrea Bonito , Wenyu Lei EMAIL logo and Joseph E. Pasciak

Abstract

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 and J. E. Pasciak, IMA J. Numer. Anal., 37 (2016), No. 3, 1245–1273] by reducing the regularity required on the data. Numerical experiments illustrating the new theory are provided.

JEL Classification: 65N30; 35S15; 65N15; 65R20; 65N12
  1. Funding: The first and second authors are partially supported by NSF grant DMS-1254618.

Acknowledgment

The authors would like to thank R. H. Nochetto for pointing out the possible suboptimality in [10], thereby prompting the current analysis.

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Received: 2017-09-18
Revised: 2018-02-01
Accepted: 2018-03-14
Published Online: 2018-03-19
Published in Print: 2019-06-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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