{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T16:38:41Z","timestamp":1788194321209,"version":"build-2803163510"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present in this paper a new second-order consistent splitting scheme for the Navier\u2013Stokes equations with no-slip boundary conditions based on (i) the Taylor expansions at time [Formula: see text] which offer better stability than the usual expansion at time [Formula: see text], and (ii) the generalized scalar auxiliary variable (GSAV) approach which allows us to treat the nonlinear term explicitly while maintaining unconditional stability. We prove rigorously its unconditional stability in a strong norm for the time dependent Stokes equations by using a clever energy argument. Using this strong stability result combined with a weak stability offered by the GSAV approach, we are able to establish, for the first time, a global-in-time optimal error estimate in two dimensions and a local-in-time error estimate in three dimensions for a second-order consistent method for the Navier\u2013Stokes equations.<\/jats:p>","DOI":"10.1137\/23m1556022","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T04:46:06Z","timestamp":1697604366000},"page":"2408-2433","source":"Crossref","is-referenced-by-count":25,"title":["Stability and Error Analysis of a Second-Order Consistent Splitting Scheme for the Navier\u2013Stokes Equations"],"prefix":"10.1137","volume":"61","author":[{"given":"Fukeng","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematics, National University of Singapore, Singapore, 119076."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4885-5732","authenticated-orcid":true,"given":"Jie","family":"Shen","sequence":"additional","affiliation":[{"name":"Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo, Zhejiang, 315200, People\u2019s Republic of China, and Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,10,18]]},"reference":[{"key":"ref1","series-title":"Springer Ser. 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