01420nas a2200145   4500008004100000020001400041245006200055210006000117300001400177490000800191520099600199100001701195700001501212856004701227       2020                        eng d  a0945-324500aA priori error estimates of regularized elliptic problems0 apriori error estimates of regularized elliptic problems  a571–5960 v1463 aApproximations 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.1 aHeltai, Luca1 aLei, Wenyu  uhttps://doi.org/10.1007/s00211-020-01152-w