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Numer. Anal."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We consider the numerical approximation of single-phase flow in porous media by a mixed finite element method with mass lumping. Our work extends previous results of Wheeler and Yotov, who showed that inexact numerical integration together with an appropriate choice of basis leads to some sort of mass lumping which allows eliminating the flux variables locally and reducing the mixed problem to a finite volume discretization for the pressure only. Here we construct second-order approximations for hybrid meshes in two and three space dimensions which, similar to the method of Wheeler and Yotov, allow the local elimination of the flux variables. A full convergence analysis of the method is given for which new arguments and, in part, also new quadrature rules and finite elements are required. The analysis formally also covers approximations of higher order, and third-order elements for triangles and quadrilaterals are presented.<\/jats:p>","DOI":"10.1137\/19m1236862","type":"journal-article","created":{"date-parts":[[2020,6,17]],"date-time":"2020-06-17T11:20:37Z","timestamp":1592392837000},"page":"1822-1844","source":"Crossref","is-referenced-by-count":4,"title":["On a Second-Order Multipoint Flux Mixed Finite Element Methods on Hybrid Meshes"],"prefix":"10.1137","volume":"58","author":[{"given":"Herbert","family":"Egger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bogdan","family":"Radu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,6,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595293582"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-007-9056-8"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202519500167"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994262585"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5"},{"key":"atypb6","first-page":"129","volume":"2","author":"Brezzi F.","year":"1974","journal-title":"RAIRO Anal. 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