{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:28:12Z","timestamp":1787329692943,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The Green function of the Poisson equation in two dimensions is not contained in the Sobolev space $H^1(\\Omega)$ such that finite element error estimates for the discretization of a problem with the Dirac measure on the right hand-side are nonstandard and quasi-uniform meshes are inappropriate. By using graded meshes $L^2$-error estimates of almost optimal order are shown. As a byproduct, we show for the Poisson equation with a right-hand side in $L^2$ that appropriate mesh refinement near some interior point diminishes the error at this point by nearly one order.<\/jats:p>","DOI":"10.1137\/090778018","type":"journal-article","created":{"date-parts":[[2011,5,20]],"date-time":"2011-05-20T13:00:06Z","timestamp":1305896406000},"page":"992-1005","source":"Crossref","is-referenced-by-count":42,"title":["A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side"],"prefix":"10.1137","volume":"49","author":[{"given":"Thomas","family":"Apel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olaf","family":"Benedix","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dieter","family":"Sirch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boris","family":"Vexler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,5,19]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(19960110)19:1<63::AID-MMA764>3.0.CO;2-S"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0041-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165003"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492901000010"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-008-9200-y"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389461"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0324078"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-008-0113-0"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0777268-5"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0777267-3"},{"key":"R11","unstructured":"J. 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