{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T00:40:05Z","timestamp":1718412005721},"reference-count":22,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The<jats:inline-formula id=\"j_cmam-2016-0004_eq_9999_w2aab3b7d149b1b6b1aab1c13b1b1Aa\"><jats:alternatives><m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><m:msup><m:mi>C<\/m:mi><m:mn>1<\/m:mn><\/m:msup><\/m:math><jats:tex-math>$C^{1}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>spline spaces with degree<jats:inline-formula id=\"j_cmam-2016-0004_eq_9998_w2aab3b7d149b1b6b1aab1c13b1b3Aa\"><jats:alternatives><m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><m:mrow><m:mi>d<\/m:mi><m:mo>\u2265<\/m:mo><m:mn>5<\/m:mn><\/m:mrow><\/m:math><jats:tex-math>$d\\geq 5$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>over given triangulations are implemented in the framework of multi-variate spline theory. Based on this approach, two-level methods are proposed by using various order spline spaces for the steady state Navier\u2013Stokes equations in the stream function formulation. The proposed method can be reduced to solving a linear equation in the high-order spline space and the nonlinear equations in the low-order spline space. The convergence analysis is given based on the Newton iteration. Besides, the matrix forms of the two-level scheme are also presented. We finally tabulate the numerical results to validate and show the efficiency of the proposed two-level spline methods.<\/jats:p>","DOI":"10.1515\/cmam-2016-0004","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T15:03:18Z","timestamp":1457967798000},"page":"497-506","source":"Crossref","is-referenced-by-count":1,"title":["Two-Level Spline Approximations for Two-Dimensional Navier\u2013Stokes Equations"],"prefix":"10.1515","volume":"16","author":[{"given":"Xinping","family":"Shao","sequence":"first","affiliation":[{"name":"School of Science, Hangzhou Dianzi University, 310018, Hangzhou, P.\u2009R. China"}]},{"given":"Danfu","family":"Han","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hangzhou Normal University, 310006, Hangzhou, P.\u2009R. China"}]},{"given":"Xianliang","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Zhejiang University, 310027, Hangzhou, P.\u2009R. 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