{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T14:01:27Z","timestamp":1743084087568,"version":"3.40.3"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319107042"},{"type":"electronic","value":"9783319107059"}],"license":[{"start":{"date-parts":[[2014,10,31]],"date-time":"2014-10-31T00:00:00Z","timestamp":1414713600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2014,10,31]],"date-time":"2014-10-31T00:00:00Z","timestamp":1414713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-10705-9_36","type":"book-chapter","created":{"date-parts":[[2014,12,2]],"date-time":"2014-12-02T14:51:54Z","timestamp":1417531914000},"page":"367-375","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiscale Adaptive Method for Stokes Flow in Heterogenenous Media"],"prefix":"10.1007","author":[{"given":"Assyr","family":"Abdulle","sequence":"first","affiliation":[]},{"given":"Ondrej","family":"Bud\u00e1\u010d","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,31]]},"reference":[{"issue":"2","key":"36_CR1","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1137\/040607137","volume":"4","author":"A. Abdulle","year":"2005","unstructured":"A. Abdulle, On a priori error analysis of fully discrete heterogeneous multiscale FEM. Multiscale Model. Simul. 4(2), 447\u2013459 (2005)","journal-title":"Multiscale Model. Simul."},{"key":"36_CR2","doi-asserted-by":"crossref","unstructured":"______________\u2009, A priori and a posteriori error analysis for numerical homogenization: a unified framework. Ser. Contemp. Appl. Math. CAM 16, 280\u2013305 (2011)","DOI":"10.1142\/9789814366892_0009"},{"key":"36_CR3","unstructured":"A. Abdulle, O. Bud\u00e1\u010d, An Adaptive Finite Element Heterogeneous Multiscale Method for the Stokes Problem in Porous Media. MATHICSE Report 41.2013, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 2013"},{"key":"36_CR4","doi-asserted-by":"crossref","unstructured":"A. Abdulle, W.E, B. Engquist, E. Vanden-Eijnden, The heterogeneous multiscale method. Acta Numer. 21, 1\u201387 (2012)","DOI":"10.1017\/S0962492912000025"},{"issue":"37\u201340","key":"36_CR5","doi-asserted-by":"publisher","first-page":"2710","DOI":"10.1016\/j.cma.2010.06.012","volume":"200","author":"A. Abdulle","year":"2011","unstructured":"A. Abdulle, A. Nonnenmacher, Adaptive finite element heterogeneous multiscale method for homogenization problems. Comput. Methods Appl. Mech. Eng. 200(37\u201340), 2710\u20132726 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"36_CR6","doi-asserted-by":"crossref","unstructured":"___________________________\u2009, A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method. Numer. Methods Partial Differ. Equ. 29(5), 1629\u20131656 (2013)","DOI":"10.1002\/num.21769"},{"issue":"3","key":"36_CR7","first-page":"203","volume":"2","author":"G. Allaire","year":"1989","unstructured":"G. Allaire, Homogenization of the Stokes flow in a connected porous medium. Asymptot. Anal. 2(3), 203\u2013222 (1989)","journal-title":"Asymptot. Anal."},{"issue":"1","key":"36_CR8","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1137\/120885541","volume":"12","author":"S. Alyaev","year":"2014","unstructured":"S. Alyaev, E. Keilegavlen, J.M. Nordbotten, Analysis of Control Volume Heterogeneous Multiscale Methods for Single Phase Flow in Porous Media. Multiscale Model. Simul. 12(1), 335\u2013363 (2014)","journal-title":"Multiscale Model. Simul."},{"issue":"2","key":"36_CR9","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/S1064827597323373","volume":"22","author":"D.N. Arnold","year":"2000","unstructured":"D.N. Arnold, A. Mukherjee, L. Pouly, Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput. 22(2), 431\u2013448 (2000)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"36_CR10","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1137\/110858525","volume":"11","author":"D.L. Brown","year":"2013","unstructured":"D.L. Brown, Y. Efendiev, V.H. Hoang, An efficient hierarchical multiscale finite element method for Stokes equations in slowly varying media. Multiscale Model. Simul. 11(1), 30\u201358 (2013)","journal-title":"Multiscale Model. Simul."},{"key":"36_CR11","unstructured":"P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Studies in Mathematics and Its Applications, vol. 4 (North-Holland, Amsterdam\/New York, 1978)"},{"key":"36_CR12","doi-asserted-by":"crossref","unstructured":"W. E, B. Engquist, The heterogeneous multiscale methods. Commun. Math. Sci. 1(1), 87\u2013132 (2003)","DOI":"10.4310\/CMS.2003.v1.n1.a8"},{"key":"36_CR13","unstructured":"W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2(3), 367\u2013450 (2007)"},{"issue":"11","key":"36_CR14","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1002\/nme.2579","volume":"79","author":"C. Geuzaine","year":"2009","unstructured":"C. Geuzaine, J.-F. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309\u20131331 (2009)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"3","key":"36_CR15","first-page":"661","volume":"10","author":"E. Maru\u0161i\u0107-Paloka","year":"1996","unstructured":"E. Maru\u0161i\u0107-Paloka, A. Mikeli\u0107, An error estimate for correctors in the homogenization of the Stokes and Navier-Stokes equations in a porous medium. Boll. Unione Mat. Ital. 10(3), 661\u2013671 (1996)","journal-title":"Boll. Unione Mat. Ital."},{"key":"36_CR16","unstructured":"A. Nonnenmacher, Adaptive finite element methods for multiscale partial differential equations, Ph.D. thesis, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 2011"},{"issue":"1","key":"36_CR17","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1137\/040605229","volume":"4","author":"M. Ohlberger","year":"2005","unstructured":"M. Ohlberger, A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems. Multiscale Model. Simul. 4(1), 88\u2013114 (2005)","journal-title":"Multiscale Model. Simul."},{"issue":"2","key":"36_CR18","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1137\/040606028","volume":"27","author":"J. Peters","year":"2005","unstructured":"J. Peters, V. Reichelt, A. Reusken, Fast iterative solvers for discrete Stokes equations. SIAM J. Sci. Comput. 27(2), 646\u2013666 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"36_CR19","unstructured":"E. S\u00e1nchez-Palencia, Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127 (Springer, Berlin\/New York, 1980)"},{"key":"36_CR20","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.cma.2013.03.025","volume":"261\u2013262","author":"C. Sandstr\u00f6m","year":"2013","unstructured":"C. Sandstr\u00f6m, F. Larsson, K. Runesson, H. Johansson, A two-scale finite element formulation of Stokes flow in porous media. Comput. Methods Appl. Mech. Eng. 261\u2013262, 96\u2013104 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"36_CR21","unstructured":"L. Tartar, Incompressible Fluid Flow in a Porous Medium\u2014Convergence of the Homogenization Process, Appendix of [19], pp. 368\u2013377 (1979)"},{"issue":"3","key":"36_CR22","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/BF01390056","volume":"55","author":"R. Verf\u00fcrth","year":"1989","unstructured":"R. Verf\u00fcrth, A posteriori error estimators for the Stokes equations. Numer. Math. 55(3), 309\u2013325 (1989)","journal-title":"Numer. Math."}],"container-title":["Lecture Notes in Computational Science and Engineering","Numerical Mathematics and Advanced Applications - ENUMATH 2013"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-10705-9_36","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T17:33:17Z","timestamp":1676914397000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-10705-9_36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,31]]},"ISBN":["9783319107042","9783319107059"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-10705-9_36","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2014,10,31]]},"assertion":[{"value":"31 October 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}