TY - JOUR
T1 - Approximation of the spectral fractional powers of the Laplace-Beltrami Operator
JF - arXiv preprint arXiv:2101.05141
Y1 - 2021
A1 - Bonito, Andrea
A1 - Wenyu Lei
ER -
TY - JOUR
T1 - Finite element approximation of an obstacle problem for a class of integroâ€“differential operators
JF - ESAIM: Mathematical Modelling and Numerical Analysis
Y1 - 2020
A1 - Bonito, Andrea
A1 - Wenyu Lei
A1 - Salgado, Abner J
PB - EDP Sciences
VL - 54
ER -
TY - JOUR
T1 - Numerical approximation of the integral fractional Laplacian
JF - Numerische Mathematik
Y1 - 2019
A1 - Bonito, Andrea
A1 - Wenyu Lei
A1 - Joseph E Pasciak
AB - We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The numerical approximation of the action of the corresponding stiffness matrix consists of three steps: (1) apply a sinc quadrature scheme to approximate the integral representation by a finite sum where each term involves the solution of an elliptic partial differential equation defined on the entire space, (2) truncate each elliptic problem to a bounded domain, (3) use the finite element method for the space approximation on each truncated domain. The consistency error analysis for the three steps is discussed together with the numerical implementation of the entire algorithm. The results of computations are given illustrating the error behavior in terms of the mesh size of the physical domain, the domain truncation parameter and the quadrature spacing parameter.
VL - 142
SN - 0945-3245
UR - https://doi.org/10.1007/s00211-019-01025-x
ER -
TY - JOUR
T1 - On sinc quadrature approximations of fractional powers of regularly accretive operators
JF - Journal of Numerical Mathematics
Y1 - 2018
A1 - Bonito, Andrea
A1 - Wenyu Lei
A1 - Joseph E Pasciak
PB - De Gruyter
ER -
TY - JOUR
T1 - The approximation of parabolic equations involving fractional powers of elliptic operators
JF - J. Comput. Appl. Math.
Y1 - 2017
A1 - Bonito, Andrea
A1 - Wenyu Lei
A1 - Joseph E Pasciak
VL - 315
UR - http://dx.doi.org/10.1016/j.cam.2016.10.016
ER -
TY - JOUR
T1 - Numerical approximation of space-time fractional parabolic equations
JF - Comput. Methods Appl. Math.
Y1 - 2017
A1 - Bonito, Andrea
A1 - Wenyu Lei
A1 - Joseph E Pasciak
VL - 17
UR - https://doi.org/10.1515/cmam-2017-0032
ER -