{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T17:13:16Z","timestamp":1648746796027},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T00:00:00Z","timestamp":1109635200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2005,3]]},"DOI":"10.1007\/bf02810621","type":"journal-article","created":{"date-parts":[[2008,1,14]],"date-time":"2008-01-14T10:24:46Z","timestamp":1200306286000},"page":"155-172","source":"Crossref","is-referenced-by-count":0,"title":["Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations"],"prefix":"10.1007","volume":"38","author":[{"given":"Michael M. J.","family":"Proot","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc I.","family":"Gerritsma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"169","key":"BF02810621_CR1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1090\/S0025-5718-1985-0771030-5","volume":"44","author":"A.K. Aziz","year":"1985","unstructured":"A.K. Aziz, R.B. Kellogg and A.B. Stephens, Least-squares methods for elliptic systems, Math. Comput. 44(169) (1985) 53\u201370.","journal-title":"Math. Comput."},{"key":"BF02810621_CR2","unstructured":"C. Bernardi and Y. Maday,Approximations spectrale de probl\u00e8mes aux limites \u00e9lliptiques (Springer-Verlag, 1992)."},{"issue":"5","key":"BF02810621_CR3","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1137\/S0036142994276001","volume":"34","author":"P.B. Bochev","year":"1997","unstructured":"P.B. Bochev, Analysis of least-squares finite element methods for the Navier-Stokes equations, SIAM J. Numer. Anal. 34(5) (1997) 1817\u20131844","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"BF02810621_CR4","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0893-9659(93)90007-A","volume":"6","author":"P.B. Bochev","year":"1993","unstructured":"P.B. Bochev and M.D. Gunzburger, A least squares finite element method for the Navier-Stokes equations, App. Math. Lett. 6(2) (1993) 27\u201330.","journal-title":"App. Math. Lett."},{"issue":"208","key":"BF02810621_CR5","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1090\/S0025-5718-1994-1257573-4","volume":"63","author":"P.B. Bochev","year":"1994","unstructured":"P.B. Bochev and M.D. Gunzburger, Analysis of least squares finite element methods for the Stokes equations, Math. Comput. 63(208) (1994) 479\u2013506.","journal-title":"Math. Comput."},{"issue":"4","key":"BF02810621_CR6","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1137\/S0036144597321156","volume":"40","author":"P.B. Bochev","year":"1998","unstructured":"P.B. Bochev and M.D. Gunzburger, Finite element methods of leasta-squares type, SIAM Rev. 40(4) (1998) 789\u2013837.","journal-title":"SIAM Rev."},{"issue":"4","key":"BF02810621_CR7","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/S0045-7930(98)00002-4","volume":"27","author":"O. Botella","year":"1998","unstructured":"O. Botella and R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27(4) (1998) 421\u2013433.","journal-title":"Comput. Fluids"},{"issue":"6","key":"BF02810621_CR8","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1137\/0731091","volume":"31","author":"Z. Cai","year":"1994","unstructured":"Z. Cai, R. Lazarov, T.A. Manteuffel and S.F. McCormick, First-order system least-squares for secondorder partial differential equations: Part I, SIAM J. Numer. Anal. 31(6) (1994) 1785\u20131799.","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02810621_CR9","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1002\/nme.1620240705","volume":"24","author":"G.F. Carey","year":"1987","unstructured":"G.F. Carey and B.-N. Jiang, Least-squares finite element method and preconditioned conjugate gradient solution, Int. J. Numer. Methods Eng. 24 (1987) 1283\u20131296.","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"207","key":"BF02810621_CR10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1090\/S0025-5718-1994-1234425-7","volume":"63","author":"C.L. Chang","year":"1994","unstructured":"C.L. Chang, An error estimate of the least-squares finite element method for the Stokes problem in three dimensions, Math. Comput. 63(207) (1994) 41\u201350.","journal-title":"Math. Comput."},{"issue":"3","key":"BF02810621_CR11","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0045-7825(90)90079-2","volume":"84","author":"C.L. Chang","year":"1990","unstructured":"C.L. Chang and B.-N. Jiang, An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for the Stokes problem, Comput. Methods Appl. Mech. Engrg. 84(3) (1990) 247\u2013255.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"BF02810621_CR12","unstructured":"W. Couzy, Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers, PhD thesis, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (1995)."},{"issue":"3","key":"BF02810621_CR13","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1137\/S1064827595294526","volume":"20","author":"J.M. Deang","year":"1998","unstructured":"J.M. Deang and M.D. Gunzburger, Issues related to least-squares finite element methods for the Stokes equations, SIAM J. Sci. Comput. 20(3) (1998) 878\u2013906.","journal-title":"SIAM J. Sci. Comput."},{"key":"BF02810621_CR14","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0021-9991(82)90058-4","volume":"48","author":"U. Ghia","year":"1982","unstructured":"U. Ghia, K.N. Ghia and C.T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48 (1982) 387\u2013411.","journal-title":"J. Comput. Phys."},{"key":"BF02810621_CR15","series-title":"Leccture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/978-3-662-03882-6_3","volume-title":"High-order Methods for Computational Physics","author":"R.D. Henderson","year":"1999","unstructured":"R.D. Henderson, Adaptive spectral element methods for turbulence and transition, in:High-order Methods for Computational Physics, Leccture Notes in Computer Science, Vol. 9, (Springer, New York, 1999) pp. 225\u2013324."},{"issue":"7","key":"BF02810621_CR16","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1002\/fld.1650140706","volume":"14","author":"B.-N. Jiang","year":"1992","unstructured":"B.-N. Jiang, A least-squares finite element method for incompressible Navier-Stokes problems, Int. J. Numer. Methods Fluids 14(7) (1992) 843\u2013859.","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"BF02810621_CR17","doi-asserted-by":"crossref","unstructured":"B-N. Jiang,The Least-Squares Finite Element Method, Theory and Applications in Computational Fluid Dynamics and Electromagnetics (Springer, 1998).","DOI":"10.1007\/978-3-662-03740-9_14"},{"issue":"1\u20132","key":"BF02810621_CR18","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0045-7825(97)00192-8","volume":"152","author":"B.-N. Jiang","year":"1998","unstructured":"B.-N. Jiang, On the least-squares method, Comput. Methods Appl. Mech. Engrg. 152(1\u20132) (1998) 239\u2013257.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"3","key":"BF02810621_CR19","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0045-7825(90)90003-5","volume":"78","author":"B.-N. Jiang","year":"1990","unstructured":"B.-N. Jiang and C.L. Chang, Least-squares finite elements for the Stokes problem, Comput. Methods Appl. Mech. Engrg. 78(3) (1990) 297\u2013311.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"3\u20134","key":"BF02810621_CR20","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0045-7825(94)90172-4","volume":"114","author":"B.-N. Jiang","year":"1994","unstructured":"B.-N. Jiang, T.L. Lin and L.A. Povinelli, Large-scale computation of incompressible viscous flow by least-squares finite element method. Comput. Methods Appl. Mech. Engrg. 114(3\u20134) (1994) 213\u2013231.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"1","key":"BF02810621_CR21","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0045-7825(90)90139-D","volume":"81","author":"B.-N. Jiang","year":"1990","unstructured":"B.-N. Jiang and L. Povinelli, Least-squares finite element method for fluid dynamics, Comput. Methods. Appl. Mech. Engrg. 81(1) (1990) 13\u201337.","journal-title":"Comput. Methods. Appl. Mech. Engrg."},{"key":"BF02810621_CR22","unstructured":"G.E. Karniadakis and S.J. Sherwin,Spectral\/hp Element Methods for CFD (Oxford University Press, 1999)."},{"key":"BF02810621_CR23","unstructured":"Y. Maday and A.T. Patera, Spectral element methods for the incompressible Navier-Stokes equations, in:State-of-the-Art Surveys in Computational Mechanics, eds. A.K. Noorr and J.T. Oden (1989). pp. 71\u2013143."},{"key":"BF02810621_CR24","doi-asserted-by":"crossref","unstructured":"J.C. Mason and D.C. Handscomb,Chebyshev Polynomials (Chapman and Hall\/CRC, 2003).","DOI":"10.1201\/9781420036114"},{"key":"BF02810621_CR25","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/S0021-9991(03)00296-1","volume":"190","author":"J.P. Pontaza","year":"2003","unstructured":"J.P. Pontaza and J.N. Reddy, Spectral\/hp least-squares finite element formulation for the Navier-Stokes equations, J. Comput. Phys. 190 (2003) 523\u2013549.","journal-title":"J. Comput. Phys."},{"key":"BF02810621_CR26","unstructured":"M.M.J. Proot, The least-squares spectral element method, PhD thesis, Delft University of Technology (2003)."},{"issue":"1\u20133","key":"BF02810621_CR27","first-page":"311","volume":"17","author":"M.M.J. Proot","year":"2002","unstructured":"M.M.J. Proot and M.I. Gerritsma, A least-squares spectral element formulation for the Stokes problem, J. Sci. Comput. 17(1\u20133) (2002) 311\u2013322.","journal-title":"J. Sci. Comput."},{"issue":"2","key":"BF02810621_CR28","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1006\/jcph.2002.7137","volume":"181","author":"M.M.J. Proot","year":"2002","unstructured":"M.M.J. Proot and M.I. Gerritsma, Least-squares spectral elements applied to the Stokes problem, J. Comput. Phys. 181(2) (2002), 454\u2013477.","journal-title":"J. Comput. Phys."},{"key":"BF02810621_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01061264","volume":"4","author":"W.W. Schultz","year":"1989","unstructured":"W.W. Schultz, N.Y. Lee and J.P. Boyd, Chebyshev pseudospectral method of viscous flows with corner singularities, J. Sci. Comput. 4 (1989) 1\u201324.","journal-title":"J. Sci. Comput."},{"issue":"1","key":"BF02810621_CR30","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0021-9991(91)90136-9","volume":"94","author":"M.R. Schumack","year":"1991","unstructured":"M.R. Schumack, W.W. Schultz and J.P. Boyd, Spectral method solution of the Stokes equations on nonstaggered grid, J. Comput. Phys. 94(1) (1991) 30\u201358.","journal-title":"J. Comput. Phys."},{"issue":"4","key":"BF02810621_CR31","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1002\/fld.515","volume":"42","author":"X.Y. Zhao","year":"2003","unstructured":"X.Y. Zhao and S.J. Liao, A short note on the general boundary element method for viscous flows with high Reynolds number, Internat J. Numer. Meth. Fluids 42(4) (2003) 349\u2013359.","journal-title":"Internat J. Numer. Meth. Fluids"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02810621.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02810621\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02810621","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T07:51:53Z","timestamp":1558252313000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02810621"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":31,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2005,3]]}},"alternative-id":["BF02810621"],"URL":"https:\/\/doi.org\/10.1007\/bf02810621","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}