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The application of these estimates to the numerical solution of elliptic problems with singularly supported forcing terms allows us to provide sharp <jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>H<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> 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.<\/jats:p>","DOI":"10.1007\/s00211-020-01152-w","type":"journal-article","created":{"date-parts":[[2020,9,29]],"date-time":"2020-09-29T22:02:37Z","timestamp":1601416957000},"page":"571-596","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A priori error estimates of regularized elliptic problems"],"prefix":"10.1007","volume":"146","author":[{"given":"Luca","family":"Heltai","sequence":"first","affiliation":[]},{"given":"Wenyu","family":"Lei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,29]]},"reference":[{"issue":"4","key":"1152_CR1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1515\/jnma-2018-0054","volume":"26","author":"G Alzetta","year":"2018","unstructured":"Alzetta, G., Arndt, D., Bangerth, W., Boddu, V., Brands, B., Davydov, D., Gassm\u00f6ller, R., Heister, T., Heltai, L., Kormann, K., Kronbichler, M., Maier, M., Pelteret, J.P., Turcksin, B., Wells, D.: The deal.II library, version 9.0. 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