{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:23:36Z","timestamp":1759191816436,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,5,13]],"date-time":"2021-05-13T00:00:00Z","timestamp":1620864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,13]],"date-time":"2021-05-13T00:00:00Z","timestamp":1620864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["EMR\/2016\/003412"],"award-info":[{"award-number":["EMR\/2016\/003412"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s11075-021-01117-6","type":"journal-article","created":{"date-parts":[[2021,5,13]],"date-time":"2021-05-13T03:41:16Z","timestamp":1620877276000},"page":"341-369","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized local projection stabilized nonconforming finite element methods for Darcy equations"],"prefix":"10.1007","volume":"89","author":[{"given":"Deepika","family":"Garg","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1858-3972","authenticated-orcid":false,"given":"Sashikumaar","family":"Ganesan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,13]]},"reference":[{"issue":"2","key":"1117_CR1","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s00211-013-0562-4","volume":"126","author":"RE Bank","year":"2014","unstructured":"Bank, RE, Yserentant, H: On the H1-stability of the L2-projection onto finite element spaces. Numer. Math. 126(2), 361\u2013381 (2014)","journal-title":"Numer. Math."},{"issue":"4","key":"1117_CR2","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s10092-001-8180-4","volume":"38","author":"R Becker","year":"2001","unstructured":"Becker, R, Braack, M: A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38(4), 173\u2013199 (2001)","journal-title":"Calcolo"},{"issue":"3","key":"1117_CR3","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1137\/S1064827595289303","volume":"20","author":"L Bergamaschi","year":"1998","unstructured":"Bergamaschi, L, Mantica, S, Manzini, G: A mixed finite element-finite volume formulation of the black-oil model. SIAM J. Sci. Comput. 20 (3), 970\u2013997 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1117_CR4","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1515\/cmam-2018-0020","volume":"19","author":"R Biswas","year":"2019","unstructured":"Biswas, R, Dond, AK, Gudi, T: Edge patch-wise local projection stabilized nonconforming FEM for the Oseen problem. Comput Methods Appl. Math. 19(2), 189\u2013214 (2019)","journal-title":"Comput Methods Appl. Math."},{"issue":"4\u20135","key":"1117_CR5","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s00466-006-0036-y","volume":"38","author":"PB Bochev","year":"2006","unstructured":"Bochev, PB, Dohrmann, CR: A computational study of stabilized, low-order C0 finite element approximations of Darcy equations. Comput. Mech. 38(4\u20135), 323\u2013333 (2006)","journal-title":"Comput. Mech."},{"issue":"2","key":"1117_CR6","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1002\/cnm.957","volume":"24","author":"PB Bochev","year":"2008","unstructured":"Bochev, P B, Gunzburger, MD: A locally conservative least-squares method for Darcy flows. Commun. Numer. Methods Eng. 24(2), 97\u2013110 (2008)","journal-title":"Commun. Numer. Methods Eng."},{"issue":"2","key":"1117_CR7","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1137\/060653494","volume":"48","author":"M Braack","year":"2009","unstructured":"Braack, M.: Optimal control in fluid mechanics by finite elements with symmetric stabilization. SIAM J. Control Optim. 48(2), 672\u2013687 (2009)","journal-title":"SIAM J. Control Optim."},{"issue":"6","key":"1117_CR8","doi-asserted-by":"publisher","first-page":"2544","DOI":"10.1137\/050631227","volume":"43","author":"M Braack","year":"2006","unstructured":"Braack, M., Burman, E.: Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. SIAM J. Numer. Anal. 43(6), 2544\u20132566 (2006)","journal-title":"SIAM J. Numer. Anal."},{"issue":"9\u201312","key":"1117_CR9","doi-asserted-by":"publisher","first-page":"1126","DOI":"10.1016\/j.cma.2010.06.034","volume":"200","author":"M Braack","year":"2011","unstructured":"Braack, M, Schieweck, F: Equal-order finite elements with local projection stabilization for the Darcy\u2013Brinkman equations. Comput. Methods Appl. Mech. Eng. 200(9\u201312), 1126\u20131136 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1117_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","author":"SC Brenner","year":"2008","unstructured":"Brenner, S.C., Scott, LR: The mathematical theory of finite element methods. Springer, New York (2008)"},{"issue":"2","key":"1117_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/BF01389710","volume":"47","author":"F Brezzi","year":"1985","unstructured":"Brezzi, F, Douglas, J. Jr., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47(2), 217\u2013235 (1985)","journal-title":"Numer. Math."},{"issue":"2","key":"1117_CR12","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/BF01396752","volume":"51","author":"F Brezzi","year":"1987","unstructured":"Brezzi, F, Douglas, J, Dur\u00e1n, R, Fortin, M: Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51(2), 237\u2013250 (1987)","journal-title":"Numer. Math."},{"issue":"4","key":"1117_CR13","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1051\/m2an\/1987210405811","volume":"21","author":"F Brezzi","year":"1987","unstructured":"Brezzi, F., Fortin, M., Marini, L.D., et al.: Efficient rectangular mixed finite elements in two and three space variables. ESAIM Math. Model. Numer. Anal. 21(4), 581\u2013604 (1987)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"1","key":"1117_CR14","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1051\/m2an:2007007","volume":"41","author":"E Burman","year":"2007","unstructured":"Burman, E., Ern, A.: A continuous finite element method with face penalty to approximate Friedrichs\u2019 systems. M2AN Math. Model. Numer. Anal. 41(1), 55\u201376 (2007)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"5","key":"1117_CR15","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1002\/num.20076","volume":"21","author":"E Burman","year":"2005","unstructured":"Burman, E., Hansbo, P.: Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. Numer. Methods Partial Differ. Equ. 21(5), 986\u2013997 (2005)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"23\u201324","key":"1117_CR16","doi-asserted-by":"publisher","first-page":"2881","DOI":"10.1016\/j.cma.2004.11.033","volume":"195","author":"E Burman","year":"2006","unstructured":"Burman, E., Hansbo, P.: A stabilized non-conforming finite element method for incompressible flow. Comput. Methods Appl. Mech. Eng. 195(23\u201324), 2881\u20132899 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"1117_CR17","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.cam.2005.11.022","volume":"198","author":"E Burman","year":"2007","unstructured":"Burman, E., Hansbo, P.: A unified stabilized method for Stokes\u2019 and Darcy\u2019s equations. J. Comput. Appl. Math. 198(1), 35\u201351 (2007)","journal-title":"J. Comput. Appl. Math."},{"issue":"1\u20132","key":"1117_CR18","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0045-7825(84)90049-5","volume":"47","author":"G Chavent","year":"1984","unstructured":"Chavent, G, Cohen, G, Jaffre, J: Discontinuous upwinding and mixed finite elements for two-phase flows in reservoir simulation. Comput. Methods Appl. Mech. Eng. 47(1\u20132), 93\u2013118 (1984)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1117_CR19","volume-title":"Finite element methods and their applications","author":"Z Chen","year":"2005","unstructured":"Chen, Z.: Finite element methods and their applications. Springer Science & Business Media, New York (2005)"},{"issue":"R-3","key":"1117_CR20","first-page":"33","volume":"7","author":"M Crouzeix","year":"1973","unstructured":"Crouzeix, M., Raviart, P. -A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r Rouge 7(R-3), 33\u201375 (1973)","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r Rouge"},{"key":"1117_CR21","volume-title":"Mathematical aspects of discontinuous Galerkin methods, vol. 69","author":"DA Di Pietro","year":"2011","unstructured":"Di Pietro, D.A., Ern, A.: Mathematical aspects of discontinuous Galerkin methods, vol. 69. Springer Science & Business Media, New York (2011)"},{"issue":"2","key":"1117_CR22","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1002\/num.22317","volume":"35","author":"AK Dond","year":"2019","unstructured":"Dond, AK, Gudi, T.: Patch-wise local projection stabilized finite element methods for convection\u2013diffusion\u2013reaction problems. Numer. Methods Partial Differ. Equ. 35(2), 638\u2013663 (2019)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"1","key":"1117_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1011551614492","volume":"4","author":"JJr Douglas","year":"2000","unstructured":"Douglas, J. Jr, Pereira, F., Yeh, L.-M.: A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media. Comput. Geosci. 4(1), 1\u201340 (2000)","journal-title":"Comput. Geosci."},{"issue":"4","key":"1117_CR24","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1029\/94WR00061","volume":"30","author":"LJ Durlofsky","year":"1994","unstructured":"Durlofsky, L.J.: Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities. Water Resour. Res. 30(4), 965\u2013973 (1994)","journal-title":"Water Resour. Res."},{"key":"1117_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4355-5","volume-title":"Theory and practice of finite elements","author":"A Ern","year":"2004","unstructured":"Ern, A, Guermond, J L: Theory and practice of finite elements. Springer, New York (2004)"},{"issue":"1\u20132","key":"1117_CR26","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/0045-7825(84)90052-5","volume":"47","author":"RE Ewing","year":"1984","unstructured":"Ewing, R E, Heinemann, RF: Mixed finite element approximation of phase velocities in compositional reservoir simulation. Comput. Methods Appl. Mech. Eng. 47(1\u20132), 161\u2013175 (1984)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1\u20132","key":"1117_CR27","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0045-7825(84)90048-3","volume":"47","author":"RE Ewing","year":"1984","unstructured":"Ewing, R.E, Russell, T.F., Wheeler, M.F.: Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics. Comput. Methods Appl. Mech. Eng. 47(1\u20132), 73\u201392 (1984)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"264","key":"1117_CR28","doi-asserted-by":"publisher","first-page":"2039","DOI":"10.1090\/S0025-5718-08-02130-3","volume":"77","author":"S Ganesan","year":"2008","unstructured":"Ganesan, S., Matthies, G., Tobiska, L.: Local projection stabilization of equal order interpolation applied to the Stokes problem. Math Comp. 77(264), 2039\u20132060 (2008)","journal-title":"Math Comp."},{"issue":"3","key":"1117_CR29","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/s10915-008-9259-8","volume":"43","author":"S Ganesan","year":"2010","unstructured":"Ganesan, S., Tobiska, L.: Stabilization by local projection for convection\u2013diffusion and incompressible flow problems. J. Sci. Comput. 43(3), 326\u2013342 (2010)","journal-title":"J. Sci. Comput."},{"key":"1117_CR30","unstructured":"Garg, D., Ganesan, S.: Generalized local projection stabilized finite element method for Advection-reaction problems. Communicated"},{"issue":"1","key":"1117_CR31","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1093\/imanum\/21.1.165","volume":"21","author":"J-L Guermond","year":"2001","unstructured":"Guermond, J.-L.: Subgrid stabilization of Galerkin approximations of linear monotone operators. IMA J. Numer. Anal. 21(1), 165\u2013197 (2001)","journal-title":"IMA J. Numer. Anal."},{"key":"1117_CR32","doi-asserted-by":"publisher","first-page":"2916","DOI":"10.1016\/j.cma.2011.04.016","volume":"200","author":"V John","year":"2011","unstructured":"John, V., Knobloch, P., Savescu, S.B.: A posteriori optimization of parameters in stabilized methods for convection-diffusion problems\u2014Part I. Comput. Methods Appl. Mech Eng. 200, 2916\u20132929 (2011)","journal-title":"Comput. Methods Appl. Mech Eng."},{"issue":"2","key":"1117_CR33","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1137\/090767807","volume":"48","author":"P Knobloch","year":"2010","unstructured":"Knobloch, P.: A generalization of the local projection stabilization for convection-diffusion-reaction equations. SIAM J. Numer. Anal. 48(2), 659\u2013680 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1117_CR34","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1093\/imanum\/drp020","volume":"31","author":"P Knobloch","year":"2011","unstructured":"Knobloch, P., Tobiska, L.: On the stability of finite-element discretizations of convection-diffusion-reaction equations. IMA J. Numer. Anal. 31(1), 147\u2013164 (2011)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1117_CR35","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1002\/num.21706","volume":"29","author":"P Knobloch","year":"2013","unstructured":"Knobloch, P., Tobiska, L.: Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem. Numer. Methods Partial Differ. Equ. 29(1), 206\u2013225 (2013)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"1117_CR36","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1137\/S0036142901383910","volume":"40","author":"KA Mardal","year":"2002","unstructured":"Mardal, K.A., Tai, X.-C., Winther, R.: A robust finite element method for Darcy\u2013Stokes flow. SIAM J. Numer. Anal. 40(5), 1605\u20131631 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"39\u201340","key":"1117_CR37","doi-asserted-by":"publisher","first-page":"4341","DOI":"10.1016\/S0045-7825(02)00371-7","volume":"191","author":"A Masud","year":"2002","unstructured":"Masud, A., Hughes, TJR: A stabilized mixed finite element method for Darcy flow. Comput. Methods Appl. Mech. Eng. 191(39\u201340), 4341\u20134370 (2002)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"1117_CR38","first-page":"656","volume":"7","author":"K Nafa","year":"2010","unstructured":"Nafa, K.: Local projection finite element stabilization for Darcy flow. Int. J. Numer. Anal. Model. 7(4), 656\u2013666 (2010)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"1117_CR39","doi-asserted-by":"crossref","unstructured":"Raviart, P.-A., Thomas, J.-M.: A mixed finite element method for 2-nd order elliptic problems. In: Mathematical Aspects of Finite Element Methods, pp 292\u2013315. Springer (1977)","DOI":"10.1007\/BFb0064470"},{"key":"1117_CR40","unstructured":"Ross, H.-G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems, vol. 24. Springer Science & Business Media (2008)"},{"issue":"5\u20138","key":"1117_CR41","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1016\/j.cma.2008.10.016","volume":"198","author":"L Tobiska","year":"2009","unstructured":"Tobiska, L.: On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection-diffusion equations. Comput. Methods Appl. Mech. Eng. 198(5\u20138), 831\u2013837 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1117_CR42","doi-asserted-by":"publisher","unstructured":"Venkatesan, J., Ganesan, S.: Finite element computations of viscoelastic two-phase flows using local projection stabilization. Int. J. Numer. Meth Fluids. https:\/\/doi.org\/10.1002\/fld.4808 (2020)","DOI":"10.1002\/fld.4808"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01117-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-021-01117-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01117-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T17:40:26Z","timestamp":1641231626000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-021-01117-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,13]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["1117"],"URL":"https:\/\/doi.org\/10.1007\/s11075-021-01117-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2021,5,13]]},"assertion":[{"value":"29 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}