{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:18:57Z","timestamp":1753885137049,"version":"3.41.2"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"national key research and development program of china","award":["2020YFA0709800."],"award-info":[{"award-number":["2020YFA0709800."]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61907034"],"award-info":[{"award-number":["61907034"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p> In this paper, a method which reconstructs an H(div)-conforming local equilibrated flux is presented for equilibrated flux-based a posteriori error estimate for the finite element method of the second-order elliptic problem. The flux is reconstructed in the lowest-order Raviart\u2013Thomas spaces for finite element approximation. For a simplicial mesh, the reconstruction which performed on every element rather than on the patch of the elements of the mesh or on the dual mesh is achieved by solving a third (or fourth)-order linear equations on every element and a second-order linear equations on every edge or face. So, the amount of computational work is small. Numerical examples demonstratex the effectiveness and improvements of our method. <\/jats:p>","DOI":"10.1142\/s1793962322500519","type":"journal-article","created":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T15:37:34Z","timestamp":1649864254000},"source":"Crossref","is-referenced-by-count":0,"title":["Reconstruction method of equilibrated flux for <i>a posteriori<\/i> error estimate of elliptic problems"],"prefix":"10.1142","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6729-9778","authenticated-orcid":false,"given":"Feng","family":"Han","sequence":"first","affiliation":[{"name":"Northwest Institute of Nuclear Technology, Xi\u2019an, Shaanxi, 710024, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Liu","sequence":"additional","affiliation":[{"name":"Northwest Institute of Nuclear Technology, Xi\u2019an, Shaanxi, 710024, P. R. 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