A method for computing singular or nearly singular integrals on closed surfaces was presented by J. T. Beale, W. Ying, and J. R. Wilson [Comm. Comput. Phys. 20 (2016), 733--753, arXiv:1508.00265] and applied to single and double layer potentials for harmonic functions. It uses regularized kernels, a straightforward quadrature rule, and corrections added for smoothing and discretization errors. In this note we give estimates for the discretization corrections which show that they can reasonably be neglected with proper choice of numerical parameters.
A regularized truncated finite element method for degenerate parabolic stochastic PDE on non-compact graph
The Hong Kong Polytechnic University（香港理工大学）；Chalmers（查尔姆斯理工大学）；University of Technology and Economics（布达佩斯科技经济大学）；Pázmány Péter Catholic University（帕兹马尼·彼得天主教大学）；CAS AMSS-PolyU Joint Laboratory of Applied Mathematics（中科院应用数学与香港理工大学联合实验室）
Well-conditioned boundary integral equation formulations and Nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains
Stability estimates of Nyström discretizations of Helmholtz decomposition boundary integral equation formulations for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions
Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Department of Mathematics University of Crete（克里特大学数学系）；Institute for Applied and Computational Mathematics Foundation for Research and Technology-Hellas（希腊研究与技术基金会应用计算数学研究所）；Department of Mathematics University of Sussex（萨塞克斯大学数学系）
