On Sinc Quadrature Approximations of Fractional Powers of Regularly Accretive Operators

TL;DR

This paper develops an improved sinc quadrature method for approximating fractional powers of regularly accretive operators, reducing regularity requirements and providing numerical validation.

Contribution

It introduces a refined sinc quadrature scheme for fractional operator powers that enhances convergence rates and lowers data regularity assumptions.

Findings

Exponential convergence of the approximation scheme.

Reduced regularity requirements for data.

Numerical experiments confirming theoretical improvements.

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, 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.