@article {bonito2021approximation,
	title = {Approximation of the spectral fractional powers of the Laplace-Beltrami Operator},
	journal = {arXiv preprint arXiv:2101.05141},
	year = {2021},
	author = {Bonito, Andrea and Wenyu Lei}
}
@article {bonito2020finite,
	title = {Finite element approximation of an obstacle problem for a class of integro{\textendash}differential operators},
	journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
	volume = {54},
	number = {1},
	year = {2020},
	pages = {229{\textendash}253},
	publisher = {EDP Sciences},
	author = {Bonito, Andrea and Wenyu Lei and Salgado, Abner J}
}
@article {2020,
	title = {A priori error estimates of regularized elliptic problems},
	journal = {Numerische Mathematik},
	year = {2020},
	author = {Luca Heltai and Wenyu Lei}
}
@article {HL2020,
	title = {A priori error estimates of regularized elliptic problems},
	journal = {Numerische Mathematik},
	volume = {146},
	number = {3},
	year = {2020},
	pages = {571{\textendash}596},
	abstract = {Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work we show a-priori rates of convergence of this approximation process in standard Sobolev norms, with minimal regularity assumptions on the approximation of the Dirac delta distribution. The application of these estimates to the numerical solution of elliptic problems with singularly supported forcing terms allows us to provide sharp \$\$H\^1\$\$and \$\$L\^2\$\$error estimates for the corresponding regularized problem. As an application, we show how finite element approximations of a regularized immersed interface method results in the same rates of convergence of its non-regularized counterpart, provided that the support of the Dirac delta approximation is set to a multiple of the mesh size, at a fraction of the implementation complexity. Numerical experiments are provided to support our theories.},
	isbn = {0945-3245},
	doi = {10.1007/s00211-020-01152-w},
	url = {https://doi.org/10.1007/s00211-020-01152-w},
	author = {Luca Heltai and Wenyu Lei}
}
@article {BLP2019,
	title = {Numerical approximation of the integral fractional Laplacian},
	journal = {Numerische Mathematik},
	volume = {142},
	number = {2},
	year = {2019},
	pages = {235{\textendash}278},
	abstract = {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.},
	isbn = {0945-3245},
	doi = {10.1007/s00211-019-01025-x},
	url = {https://doi.org/10.1007/s00211-019-01025-x},
	author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak}
}
@article {BLP18,
	title = {On sinc quadrature approximations of fractional powers of regularly accretive operators},
	journal = {Journal of Numerical Mathematics},
	year = {2018},
	publisher = {De Gruyter},
	doi = {10.1515/jnma-2017-0116},
	author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak}
}
@article {BLP16,
	title = {The approximation of parabolic equations involving fractional powers of elliptic operators},
	journal = {J. Comput. Appl. Math.},
	volume = {315},
	year = {2017},
	pages = {32{\textendash}48},
	issn = {0377-0427},
	doi = {10.1016/j.cam.2016.10.016},
	url = {http://dx.doi.org/10.1016/j.cam.2016.10.016},
	author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak}
}
@article {BLP17a,
	title = {Numerical approximation of space-time fractional parabolic equations},
	journal = {Comput. Methods Appl. Math.},
	volume = {17},
	number = {4},
	year = {2017},
	pages = {679{\textendash}705},
	issn = {1609-4840},
	doi = {10.1515/cmam-2017-0032},
	url = {https://doi.org/10.1515/cmam-2017-0032},
	author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak}
}
