{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:57Z","timestamp":1760057877903,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we employ interpolation and projection methodologies to establish a superconvergence outcome for the Stokes problem, as approximated by the mixed finite element method (FEM) utilizing Bernstein polynomial basis functions. It is widely recognized that the convergence rate of the FEM in the L2-norm is O(hm+2). However, this paper presents an innovative superconvergence result: specifically, in terms of the L2-norm, the error convergence rate between the mixed finite element approximate solution and the local projection is O(hm+2), with m denoting the order of the Bernstein polynomial basis function.<\/jats:p>","DOI":"10.3390\/axioms14030168","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T12:01:17Z","timestamp":1740484877000},"page":"168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Superconvergence of Mixed Finite Element Method with Bernstein Polynomials for Stokes Problem"],"prefix":"10.3390","volume":"14","author":[{"given":"Lanyin","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China"}]},{"given":"Siya","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China"}]},{"given":"Ziwei","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.camwa.2023.10.035","article-title":"A three-dimensional Petrov-Galerkin finite element interface method for solving inhomogeneous anisotropic Maxwell\u2019s equations in irregular regions","volume":"152","author":"Zhao","year":"2023","journal-title":"Comput. 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