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 integro–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 - A priori error estimates of regularized elliptic problems JF - Numerische Mathematik Y1 - 2020 A1 - Luca Heltai A1 - Wenyu Lei AB - 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. VL - 146 SN - 0945-3245 UR - https://doi.org/10.1007/s00211-020-01152-w ER - TY - JOUR T1 - A priori error estimates of regularized elliptic problems JF - Numerische Mathematik Y1 - 2020 A1 - Luca Heltai A1 - Wenyu Lei 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 -