{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:38Z","timestamp":1787337218567,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper, we develop global superconvergence estimates for the lowest-order Raviart--Thomas mixed finite element method for second-order elliptic equations with general boundary conditions on triangular meshes, where most pairs of adjacent triangles form approximate parallelograms. In particular, we prove the $L^{2}$-distance between the numerical solution and canonical interpolant for the vector variable is of order $1+\\rho$, where $\\rho\\in(0,1]$ is dependent on the mesh structure. By a cheap local postprocessing operator $G_{h}$, we prove the $L^{2}$-distance between the exact solution and the postprocessed numerical solution for the vector variable is of order $1+\\rho$. As a by-product, we also obtain the superconvergence estimate for Crouzeix--Raviart nonconforming finite elements on triangular meshes of the same type.<\/jats:p>","DOI":"10.1137\/17m112587x","type":"journal-article","created":{"date-parts":[[2018,3,29]],"date-time":"2018-03-29T14:25:16Z","timestamp":1522333516000},"page":"792-815","source":"Crossref","is-referenced-by-count":14,"title":["Global Superconvergence of the Lowest-Order Mixed Finite Element on Mildly Structured Meshes"],"prefix":"10.1137","volume":"56","author":[{"given":"Yu-Wen","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,3,29]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1985190100071"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290139874X"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901398751"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/060675174"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431744-9"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050064"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(99)00034-3"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389710"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02155-8"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1985190303971"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0771029-9"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385626"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/0728054"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997322801"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0729-2"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02051-6"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00281-9"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/num.10078"},{"key":"atypb21","first-page":"115","volume":"3","author":"Lin Q.","year":"1985","journal-title":"J. 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