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Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper, a characteristics marker and cell (C-MAC) scheme is established for the Navier--Stokes equations on nonuniform grids. Error estimates for the pressure and velocity in different discrete norms are established rigorously and carefully. We obtain the second order superconvergence in the discrete $L^2$ norm for both velocity and pressure and the second order superconvergence for some terms of the $H^1$ norm of the velocity for the C-MAC scheme on nonuniform grids, which have not been reported before. Finally, some numerical experiments are presented to show the correctness and accuracy of the C-MAC scheme and the robustness and efficiency of the overall solution technique has been demonstrated using the lid-driven cavity model.<\/jats:p>","DOI":"10.1137\/18m1175069","type":"journal-article","created":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T11:00:32Z","timestamp":1526382032000},"page":"1313-1337","source":"Crossref","is-referenced-by-count":22,"title":["Superconvergence of Characteristics Marker and Cell Scheme for the Navier--Stokes Equations on Nonuniform Grids"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9245-0647","authenticated-orcid":true,"given":"Xiaoli","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongxing","family":"Rui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(19971230)25:12<1421::AID-FLD334>3.0.CO;2-A"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.07.011"},{"key":"atypb3","first-page":"1","author":"Chen H.","year":"2017","journal-title":"J. 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