{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:41Z","timestamp":1787337221885,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.<\/jats:p>","DOI":"10.1137\/17m1139333","type":"journal-article","created":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T14:34:39Z","timestamp":1523975679000},"page":"1048-1063","source":"Crossref","is-referenced-by-count":22,"title":["On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form"],"prefix":"10.1137","volume":"56","author":[{"given":"Viktor","family":"Linders","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomas","family":"Lundquist","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Nordstr\u00f6m","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597325141"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0234"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6114"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.01.038"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.10.051"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.06.014"},{"key":"atypb7","volume-title":"Conservative and Stable Degree Preserving SBP Finite Difference Operators for Non-conforming Meshes, preprint, arXiv:1611.00979","author":"Friedrich L.","year":"2016"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/120890144"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.09.013"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1975-0386296-7"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/0718014"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/15M1038360"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.07.015"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-208350-1.50012-1"},{"key":"atypb15","volume-title":"Technical report, Department of Scientific Computing","author":"Kreiss H.-O.","year":"1977"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.03.039"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.08.005"},{"key":"atypb18","unstructured":"T. Lundquist and J. Nordstr\u00f6m,\n                      On the Suboptimal Accuracy of Summation-by-Parts Schemes with Non-conforming Block Interfaces\n                      , Technical Report LiTH-MAT-R-2015\/16-SE, Link\u00f6ping University, Sweden, 2015."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.12.041"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/090750068"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.03.001"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-005-9013-4"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.02.009"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1005"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025881528802"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.02.014"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.02.031"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0468-x"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1139333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:23Z","timestamp":1787334623000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1139333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1139333"],"URL":"https:\/\/doi.org\/10.1137\/17m1139333","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}