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Some of the results covered here have been proved in previous works, coauthored with several coworkers.<\/jats:p>","DOI":"10.1515\/cmam-2017-0059","type":"journal-article","created":{"date-parts":[[2018,2,7]],"date-time":"2018-02-07T10:01:55Z","timestamp":1517997715000},"page":"477-493","source":"Crossref","is-referenced-by-count":6,"title":["Discrete Functional Analysis Tools for Some Evolution Equations"],"prefix":"10.1515","volume":"18","author":[{"given":"Thierry","family":"Gallou\u00ebt","sequence":"first","affiliation":[{"name":"Universit\u00e9 d\u2019Aix-Marseille , Marseille , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,2,7]]},"reference":[{"key":"2023033110284029320_j_cmam-2017-0059_ref_001_w2aab3b7e3508b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"H. W.  Alt and S.  Luckhaus,\nQuasilinear elliptic-parabolic differential equations,\nMath. Z. 183 (1983), no. 3, 311\u2013341.","DOI":"10.1007\/BF01176474"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_002_w2aab3b7e3508b1b6b1ab2ab2Aa","unstructured":"J.-P.  Aubin,\nUn th\u00e9or\u00e8me de compacit\u00e9,\nC. R. Acad. Sci. Paris 256 (1963), 5042\u20135044."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_003_w2aab3b7e3508b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"E.  Ch\u00e9nier, R.  Eymard, T.  Gallou\u00ebt and R.  Herbin,\nAn extension of the MAC scheme to locally refined meshes: Convergence analysis for the full tensor time-dependent Navier\u2013Stokes equations,\nCalcolo 52 (2015), 69\u2013107.","DOI":"10.1007\/s10092-014-0108-x"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_004_w2aab3b7e3508b1b6b1ab2ab4Aa","unstructured":"J.  Droniou, R.  Eymard, T.  Gallou\u00ebt, C.  Guichard and R.  Herbin,\nThe gradient discretisation method: A framework for the discretisation and numerical analysis of linear and nonlinear elliptic and parabolic problems,\npreprint (2017), https:\/\/hal.archives-ouvertes.fr\/hal-01382358\/file\/gdm.pdf."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_005_w2aab3b7e3508b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"R.  Eymard, T.  Gallou\u00ebt and R.  Herbin,\nFinite volume methods,\nHandbook of Numerical Analysis,\nNorth-Holland, Amsterdam (2000), 713\u20131020.","DOI":"10.1016\/S1570-8659(00)07005-8"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_006_w2aab3b7e3508b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"R.  Eymard, T.  Gallou\u00ebt and R.  Herbin,\nDiscretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: A scheme using stabilization and hybrid interfaces,\nIMA J. Numer. Anal. 30 (2010), no. 4, 1009\u20131043.","DOI":"10.1093\/imanum\/drn084"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_007_w2aab3b7e3508b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"T.  Gallou\u00ebt,\nSome discrete functional analysis tools,\nFinite Volumes for Complex Applications. VIII,\nSpringer Proc. Math. Stat. 199,\nSpringer, Cham (2017), 29\u201341.","DOI":"10.1007\/978-3-319-57397-7_3"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_008_w2aab3b7e3508b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"T.  Gallou\u00ebt, L.  Gastaldo, R.  Herbin and J.-C.  Latch\u00e9,\nAn unconditionally stable pressure correction scheme for the compressible barotropic Navier\u2013Stokes equations,\nM2AN Math. Model. Numer. Anal. 42 (2008), no. 2, 303\u2013331.","DOI":"10.1051\/m2an:2008005"},{"key":"2023033110284029320_j_cmam-2017-0059_ref_009_w2aab3b7e3508b1b6b1ab2ab9Aa","unstructured":"T.  Gallou\u00ebt and R.  Herbin,\nMesure, int\u00e9gration, probabilit\u00e9s,\nEllipse, Paris, 2013."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_010_w2aab3b7e3508b1b6b1ab2ac10Aa","unstructured":"T.  Gallou\u00ebt and R.  Herbin,\nEquations aux d\u00e9riv\u00e9es partielles,\nlecture notes (2015), https:\/\/hal.archives-ouvertes.fr\/cel-01196782."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_011_w2aab3b7e3508b1b6b1ab2ac11Aa","unstructured":"T.  Gallou\u00ebt, R.  Herbin, J.-C.  Latch\u00e9 and D.  Maltese,\nConvergence of the MAC scheme for the compressible stationary Navier\u2013Stokes equations,\npreprint (2017), https:\/\/arxiv.org\/abs\/1607.01968v2;\nto appear in Math. Comp."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_012_w2aab3b7e3508b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"T.  Gallou\u00ebt and J.-C.  Latch\u00e9,\nCompactness of discrete approximate solutions to parabolic PDEs\u2014application to a turbulence model,\nCommun. Pure Appl. 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Lions,\nQuelques m\u00e9thodes de r\u00e9solution des probl\u00e8mes aux limites non lin\u00e9aires,\nDunod, Paris, 1969."},{"key":"2023033110284029320_j_cmam-2017-0059_ref_016_w2aab3b7e3508b1b6b1ab2ac16Aa","doi-asserted-by":"crossref","unstructured":"J.  Simon,\nCompact sets in the space Lp(0,T;B),\nAnn. Mat. Pura Appl. 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