{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:58:49Z","timestamp":1760151529387,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601410"],"award-info":[{"award-number":["11601410"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An adaptive moving mesh method for optimal control problems in viscous incompressible fluid is proposed with the incompressible Navier\u2013Stokes system used to describe the motion of the fluid. The moving distance of nodes in the adopted mesh moving strategy is found by solving a diffusion equation with source terms, and an algorithm that fully considers the characteristics of the control problem is given with symmetry reduction to the incompressible Navier\u2013Stokes equations. Numerical examples are provided to show that the proposed algorithm can solve the optimal control problem stably and efficiently on the premise of ensuring high precision.<\/jats:p>","DOI":"10.3390\/sym14040707","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:29:15Z","timestamp":1648762155000},"page":"707","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Adaptive Moving Mesh Method for Solving Optimal Control Problems in Viscous Incompressible Fluid"],"prefix":"10.3390","volume":"14","author":[{"given":"Junxiang","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Mathematics of School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}]},{"given":"Hong","family":"Xue","sequence":"additional","affiliation":[{"name":"Department of Mathematics of School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}]},{"given":"Xianbao","family":"Duan","sequence":"additional","affiliation":[{"name":"Department of Mathematics of School of Science, Xi\u2019an University of Technology, Xi\u2019an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bonnans, J.F., and Shapiro, A. 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