01500nas a2200157 4500008004100000020001400041245006500055210006500120300001400185490000800199520103100207100001901238700001501257700002301272856004701295 2019 eng d a0945-324500aNumerical approximation of the integral fractional Laplacian0 aNumerical approximation of the integral fractional Laplacian a235–2780 v1423 aWe 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.1 aBonito, Andrea1 aLei, Wenyu1 aPasciak, Joseph, E uhttps://doi.org/10.1007/s00211-019-01025-x00517nas a2200121 4500008004100000245009200041210006900133260001500202100001900217700001500236700002300251856012100274 2018 eng d00aOn sinc quadrature approximations of fractional powers of regularly accretive operators0 asinc quadrature approximations of fractional powers of regularly bDe Gruyter1 aBonito, Andrea1 aLei, Wenyu1 aPasciak, Joseph, E uhttps://www.math.sissa.it/publication/sinc-quadrature-approximations-fractional-powers-regularly-accretive-operators00490nas a2200145 4500008004100000022001400041245009500055210006900150300001200219490000800231100001900239700001500258700002300273856004800296 2017 eng d a0377-042700aThe approximation of parabolic equations involving fractional powers of elliptic operators0 aapproximation of parabolic equations involving fractional powers a32–480 v3151 aBonito, Andrea1 aLei, Wenyu1 aPasciak, Joseph, E uhttp://dx.doi.org/10.1016/j.cam.2016.10.01600464nas a2200145 4500008004100000022001400041245007300055210006900128300001400197490000700211100001900218700001500237700002300252856004300275 2017 eng d a1609-484000aNumerical approximation of space-time fractional parabolic equations0 aNumerical approximation of spacetime fractional parabolic equati a679–7050 v171 aBonito, Andrea1 aLei, Wenyu1 aPasciak, Joseph, E uhttps://doi.org/10.1515/cmam-2017-0032