{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:53Z","timestamp":1787337233535,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>We consider the laminar viscous channel flow over a porous surface. The size of the pores is much smaller than the size of the channel, and it is important to determine the effective boundary conditions at the porous surface. We study the corresponding boundary layers, and, by a rigorous asymptotic expansion, we obtain Saffman's modification of the interface condition observed by Beavers and Joseph. The effective coefficient in the law is determined through an auxiliary boundary-layer type problem, whose computational and modeling aspects are discussed in detail. Furthermore, the approximation errors for the velocity and for the effective mass flow are given as powers of the characteristic pore size $\\ep$. Finally, we give the interface condition linking the effective pressure fields in the porous medium and in the channel, and we determine the jump of the effective pressures explicitly.<\/jats:p>","DOI":"10.1137\/s1064827599360339","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"2006-2028","source":"Crossref","is-referenced-by-count":94,"title":["Asymptotic Analysis of the Laminar Viscous Flow Over a Porous Bed"],"prefix":"10.1137","volume":"22","author":[{"given":"Willi","family":"J\u00e4ger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andro","family":"Mikelic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Neuss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0731051"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112067001375"},{"key":"R3","unstructured":"F. Brezzi, J. Pitk\u00e4ranta, On the stabilization of finite element approximations of the Stokes equations, Notes Numer. Fluid Mech., Vol. 10, Vieweg, Braunschweig, 1984, 11\u20131986j:65147"},{"key":"R4","unstructured":"R. E. Caflisch and J. Rubinstein,\n                      Lectures on the Mathematical Theory of Multiphase Flow\n                      , Lecture notes, Courant Institute of Mathematical Sciences, New York, 1984."},{"key":"R5","first-page":"73","volume":"14","author":"Ene Horia","year":"1975","journal-title":"J. M\u00e9canique"},{"key":"R6","unstructured":"W. Hackbusch,\n                      Multigrid Methods and Applications\n                      , Springer Ser. Comput. Math. 4, Springer\u2013Verlag, Berlin, 1985."},{"key":"R7","unstructured":"J. Harig,\n                      Eine robuste und effiziente Finite Elemente Methode zur L\u00f6sung der inkompressiblen 3\u2010D Navier\u2010Stokes\u2010Gleichungen auf Vektorrechnern\n                      , Ph.D. thesis, Universit\u00e4t Heidelberg, Heidelberg, Germany, 1991."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(86)90025-3"},{"key":"R9","first-page":"403","volume":"23","author":"J\u00e4ger Willi","year":"1996","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S003613999833678X"},{"key":"R11","unstructured":"W. J\u00e4ger, A. Mikeli\u0107, and N. Neuss,\n                      Asymptotic Analysis of the Laminar Viscous Flow over a Porous Bed\n                      , Tech. rep., Universit\u00e4t Heidelberg, Heidelberg, Germany, 1999."},{"key":"R11","unstructured":"IWR\u2010Preprint 1999\u201033, http:\/\/www.iwr.uni\u2010heidelberg.de\/sfb."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(75)90054-3"},{"key":"R13","volume-title":"Some methods in the mathematical analysis of systems and their control","author":"Lions J.\u2010L.","year":"1981"},{"key":"R14","unstructured":"A. Mikeli\u0107,\n                      Homogenization theory and applications to filtration through porous media\n                      , in Filtration in Porous Media and Industrial Applications, Lecture Notes in Math. 1734, M. S. Espedal, A. Fasano, and A. Mikeli\u0107, eds., Springer\u2010Verlag, Berlin, 2000, pp. 127\u2013214."},{"key":"R15","unstructured":"N. Neuss,\n                      Homogenisierung und Mehrgitter\n                      , Ph.D. thesis, Universit\u00e4t Heidelberg, Heidelberg, Germany, 1995."},{"key":"R15","unstructured":"Also as ICA\u2010Report N96\/7, ICA Stuttgart, Germany, 1996."},{"key":"R16","unstructured":"N. Neuss and C. Wieners,\n                      Criteria for the Approximation Property for Multigrid Methods in Nonnested Spaces\n                      , Tech. rep. SFB 359, Universit\u00e4t Heidelberg, Heidelberg, Germany, 2000;"},{"key":"R16","unstructured":"also available online from http:\/\/www.iwr.uni\u2010heidelberg.de\/sfb."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/sapm197150293"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01398380"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0710022"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0711031"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599360339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:29Z","timestamp":1787334689000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599360339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827599360339"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599360339","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}