On Sinc Quadrature Approximations of Fractional Powers of Regularly Accretive Operators
For researchers in numerical analysis, this provides a more efficient finite element method for fractional PDEs with weaker regularity assumptions.
The paper improves error estimates for sinc quadrature approximations of fractional powers of regularly accretive operators, reducing required data regularity while maintaining exponential convergence.
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.