{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:49:49Z","timestamp":1776721789265,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"214","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We present spectral methods for solving the Stokes problem in a circular domain. Their main feature is the uniform inf-sup condition, which allows for optimal error estimates. We apply them to the resolution of exterior problems by coupling with the transparent boundary condition.<\/p>","DOI":"10.1090\/s0025-5718-96-00710-7","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"507-531","source":"Crossref","is-referenced-by-count":6,"title":["Spectral methods in polar coordinates for the Stokes problem. Application to computation in unbounded domains"],"prefix":"10.1090","volume":"65","author":[{"given":"Laurence","family":"Halpern","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","series-title":"Math\\'{e}matiques \\& Applications (Berlin) [Mathematics \\& Applications]","isbn-type":"print","volume-title":"Approximations spectrales de probl\\`emes aux limites elliptiques","volume":"10","author":"Bernardi, Christine","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/2287003878"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1002\/fld.1650080504","article-title":"A collocation method over staggered grids for the Stokes problem","volume":"8","author":"Bernardi, Christine","year":"1988","journal-title":"Internat. J. Numer. Methods Fluids","ISSN":"https:\/\/id.crossref.org\/issn\/0271-2091","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01210846","article-title":"Large solutions for harmonic maps in two dimensions","volume":"92","author":"Brezis, Ha\u00efm","year":"1983","journal-title":"Comm. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3616","issn-type":"print"},{"issue":"4","key":"4","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/BF01389656","article-title":"Spectral methods for exterior elliptic problems","volume":"46","author":"Canuto, C.","year":"1985","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"157","key":"5","doi-asserted-by":"publisher","first-page":"67","DOI":"10.2307\/2007465","article-title":"Approximation results for orthogonal polynomials in Sobolev spaces","volume":"38","author":"Canuto, C.","year":"1982","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"6","series-title":"Computer Science and Applied Mathematics","isbn-type":"print","volume-title":"Methods of numerical integration","author":"Davis, Philip J.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0122063600","edition":"2"},{"key":"7","volume-title":"Calcul infinit\\'{e}simal","author":"Dieudonn\u00e9, Jean","year":"1968"},{"key":"8","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite element methods for Navier-Stokes equations","volume":"5","author":"Girault, Vivette","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/3540157964"},{"key":"9","unstructured":"L. Halpern, M\u00e9thodes spectrales pour la r\u00e9solution du probl\u00e8me de Stokes dans un disque, Application aux calculs en domaine non born\u00e9, Pr\u00e9publication 93-12, Universit\u00e9 Paris-Nord."},{"issue":"152","key":"10","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.2307\/2006375","article-title":"On the coupling of boundary integral and finite element methods","volume":"35","author":"Johnson, Claes","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/0021-9991(89)90041-7","article-title":"Exact nonreflecting boundary conditions","volume":"82","author":"Keller, Joseph B.","year":"1989","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"2","key":"12","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1016\/0022-0531(88)90273-6","article-title":"Stability and the Nash solution","volume":"45","author":"Lensberg, Terje","year":"1988","journal-title":"J. Econom. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-0531","issn-type":"print"},{"key":"13","unstructured":"V. Levillain, Couplage \u00e9l\u00e9ments finis-\u00e9quations int\u00e9grales pour la r\u00e9solution des \u00e9quations de Maxwell en milieu h\u00e9t\u00e9rog\u00e8ne, Th\u00e8se de doctorat de l\u2019Ecole Polytechnique, June 1991."},{"issue":"4","key":"14","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1051\/m2an\/1982160404051","article-title":"R\u00e9solution d\u2019un probl\u00e8me aux limites dans un ouvert axisym\u00e9trique par \u00e9l\u00e9ments finis en \ud835\udc5f, \ud835\udc67 et s\u00e9ries de Fourier en \ud835\udf03","volume":"16","author":"Mercier, B.","year":"1982","journal-title":"RAIRO Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0399-0516","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1002\/mma.1670050124","article-title":"The coupling of boundary integral and finite element methods for the bidimensional exterior steady Stokes problem","volume":"5","author":"Sequeira, A.","year":"1983","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"key":"16","unstructured":"G. Szeg\u00f6, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1939. MR1:14"},{"issue":"4","key":"17","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1051\/m2an\/1989230406491","article-title":"Compatibilit\u00e9 des espaces discrets pour l\u2019approximation spectrale du probl\u00e8me de Stokes p\u00e9riodique\/non p\u00e9riodique","volume":"23","author":"Vandeven, Herv\u00e9","year":"1989","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00710-7\/S0025-5718-96-00710-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00710-7\/S0025-5718-96-00710-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:06:46Z","timestamp":1776719206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00710-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":17,"journal-issue":{"issue":"214","published-print":{"date-parts":[[1996,4]]}},"alternative-id":["S0025-5718-96-00710-7"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00710-7","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}