{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T08:33:35Z","timestamp":1769330015485,"version":"3.49.0"},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11371287"],"award-info":[{"award-number":["11371287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A new numerical regularization method for the natural convection problem is presented, which is based on a type of implicit-explicit (IMEX) second-order time-stepping schemes in temporal discretization and stabilized mixed finite element in spatial discretization. This method deals with a non-linear advection term in both the momentum equation and the energy equation by linearization. We only need to solve a linear problem at each time step and the discrete curvature of the solutions is added as a stabilization term for the velocity, the pressure and the temperature, respectively. Unconditional stability is proved and an a priori error estimate is derived. Finally, a series of numerical experiments are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.<\/jats:p>","DOI":"10.1515\/cmam-2016-0006","type":"journal-article","created":{"date-parts":[[2016,2,24]],"date-time":"2016-02-24T20:59:02Z","timestamp":1456347542000},"page":"321-344","source":"Crossref","is-referenced-by-count":17,"title":["Numerical Analysis and Computation of a Type of IMEX Method for the Time-Dependent Natural Convection Problem"],"prefix":"10.1515","volume":"16","author":[{"given":"Yun-Bo","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"}]},{"given":"Yao-Lin","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2016,2,24]]},"reference":[{"key":"ref231","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s007910050051","article-title":"Large eddy simulation and the variational multiscale method Large eddy simulation and the variational multiscale methodComput","volume":"24","author":"Hughes","year":"2000","journal-title":"Comput Vis Sci Vis Sci"},{"key":"ref271","first-page":"1639","article-title":"Subgrid stabilized defect correction methods for the Navier Stokes equations SIAM Subgrid stabilized defect correction methods for the Navier Stokes equationsSIAM","volume":"28","author":"Kaya","year":"2006","journal-title":"Numer Anal Anal"},{"key":"ref411","first-page":"543","article-title":"Error analysis of a fully discrete finite element variational multiscale method for the natural convection problem Error analysis of a fully discrete finite element variational multiscale method for the natural convection problemComput","volume":"42","author":"Zhang","year":"2014","journal-title":"Comput Math Appl Math Appl"},{"key":"ref81","first-page":"381","article-title":"A projection - 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