{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T17:25:56Z","timestamp":1768584356537,"version":"3.49.0"},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Based on a hierarchical basis a posteriori error estimator,\nan adaptive weak Galerkin finite element method (WGFEM) is proposed\nfor the Stokes problem in two and three dimensions.\nIn this paper, we propose two novel diagonalization techniques for velocity and pressure, respectively.\nUsing diagonalization techniques,\nwe need only to solve two diagonal linear algebraic systems\ncorresponding to the degree of freedom to get the error\nestimator. The upper bound and lower bound of the\nerror estimator are also shown to address the reliability of the\nadaptive method. Numerical simulations are provided to demonstrate\nthe effectiveness and robustness of our algorithm.<\/jats:p>","DOI":"10.1515\/cmam-2022-0087","type":"journal-article","created":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T23:44:36Z","timestamp":1670370276000},"page":"783-811","source":"Crossref","is-referenced-by-count":1,"title":["A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques"],"prefix":"10.1515","volume":"23","author":[{"given":"Jiachuan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Physical and Mathematical Sciences , Nanjing Tech University , Nanjing 211816 , P. R. China"}]},{"given":"Ran","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics , Jilin University , Changchun 130012, Jilin , P. R. China"}]},{"given":"Jingzhi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics & National Center for Applied Mathematics , Shenzhen & SUSTech International Center for Mathematics , Southern University of Science and Technology , Shenzhen 518055 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2022,12,6]]},"reference":[{"key":"2023070413382830994_j_cmam-2022-0087_ref_001","doi-asserted-by":"crossref","unstructured":"S.  Adjerid, M.  Aiffa and J. E.  Flaherty,\nHierarchical finite element bases for triangular and tetrahedral elements,\nComput. Methods Appl. Mech. Engrg. 190 (2001), no. 22\u201323, 2925\u20132941.","DOI":"10.1016\/S0045-7825(00)00273-5"},{"key":"2023070413382830994_j_cmam-2022-0087_ref_002","doi-asserted-by":"crossref","unstructured":"J. H.  Adler, X.  Hu, L.  Mu and X.  Ye,\nAn a posteriori error estimator for the weak Galerkin least-squares finite-element method,\nJ. Comput. Appl. 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