{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T10:36:34Z","timestamp":1777545394602,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,8,19]],"date-time":"2010-08-19T00:00:00Z","timestamp":1282176000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1007\/s00607-010-0115-y","type":"journal-article","created":{"date-parts":[[2010,8,17]],"date-time":"2010-08-17T21:13:39Z","timestamp":1282079619000},"page":"217-240","source":"Crossref","is-referenced-by-count":8,"title":["Parallel least-squares finite element method for time-dependent convection\u2013diffusion system"],"prefix":"10.1007","volume":"91","author":[{"given":"Jiansong","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danping","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,8,19]]},"reference":[{"key":"115_CR1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/0045-7825(95)00826-M","volume":"126","author":"PB Bochev","year":"1995","unstructured":"Bochev PB, Gunzburger MD (1995) Least-squares method for the velocity\u2013pressure\u2013stress formulation of the Stokes equations. Comput Methods Appl Mech Eng 126: 267\u2013287","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR2","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1137\/0731091","volume":"31","author":"Z Cai","year":"1994","unstructured":"Cai Z, Lazarov R, Manteuffel TA, McCormick SF (1994) First-order least squares for second-order partial differential equations: Part I. SIAM J Numer Anal 31: 1785\u20131799","journal-title":"SIAM J Numer Anal"},{"key":"115_CR3","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1137\/0916065","volume":"16","author":"GF Carey","year":"1995","unstructured":"Carey GF, Pehlivanov AI, Vassilevski PS (1995) Least-squares mixed finite element method for non-selfadjoint elliptic problem. SIAM J Scientific Comput 16: 1126\u20131136","journal-title":"SIAM J Scientific Comput"},{"key":"115_CR4","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0096-3003(87)90037-3","volume":"23","author":"CL Chang","year":"1987","unstructured":"Chang CL (1987) A finite element method for first order elliptic system in three dimension. Appl Math Comput 23: 171\u2013183","journal-title":"Appl Math Comput"},{"key":"115_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(90)90121-2","volume":"83","author":"CL Chang","year":"1990","unstructured":"Chang CL (1990) A least-squares finite element method for the Helmholtz equation. Comput Methods Appl Mech Eng 83: 1\u20137","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR6","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1137\/0727069","volume":"27","author":"CL Chang","year":"1990","unstructured":"Chang CL, Gunzburger MD (1990) A subdomain-Galerkin\/least square method for first order elliptic system in the plane. SIAM J Numer Anal 27: 1197\u20131211","journal-title":"SIAM J Numer Anal"},{"key":"115_CR7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1090\/S0025-5718-1994-1234425-7","volume":"207","author":"CL Chang","year":"1994","unstructured":"Chang CL (1994) An error estimate of the least squares finite element method for Stokes problem in three dimension. Math Comput 207: 41\u201350","journal-title":"Math Comput"},{"key":"115_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0045-7825(95)00860-7","volume":"128","author":"CL Chang","year":"1995","unstructured":"Chang CL, Yang SY, Hsu CH (1995) A least-squares finite element method for incompressible flow in stress\u2013velocity\u2013pressure version. Comput Methods Appl Mech Eng 128: 1\u20139","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR9","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0045-7825(90)90003-5","volume":"78","author":"BN Jiang","year":"1990","unstructured":"Jiang BN, Chang CL (1990) Least squares finite element for the Stokes problem. Comput Methods Appl Mech Eng 78: 297\u2013311","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0045-7825(93)90108-A","volume":"102","author":"BN Jiang","year":"1990","unstructured":"Jiang BN, Povinelli LA (1990) Optimal least squares finite element method for elliptic problems. Comput Methods Appl Mech Eng 102: 199\u2013212","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR11","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1137\/0731071","volume":"31","author":"AI Pehlivanov","year":"1994","unstructured":"Pehlivanov AI, Carey GF, Lazarov RD (1994) Least-squares mixed finite elements for second order elliptic problems. SIAM Numer Anal 31: 1368\u20131375","journal-title":"SIAM Numer Anal"},{"key":"115_CR12","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1051\/m2an\/1994280504991","volume":"28","author":"AI Pehlivanov","year":"1994","unstructured":"Pehlivanov AI, Carey GF (1994) Error estimate for least-squares mixed finite elements. RAIRO Model Math Numer Anal 28: 499\u2013516","journal-title":"RAIRO Model Math Numer Anal"},{"key":"115_CR13","doi-asserted-by":"crossref","first-page":"3591","DOI":"10.1002\/nme.1620382104","volume":"38","author":"ST Yu","year":"1995","unstructured":"Yu ST, Jiang BN, Liu NS, Wu J (1995) The least-squares finite element method for low-Mach-number compressible viscous flows. Int J Numer Methods Fluids 38: 3591\u20133610","journal-title":"Int J Numer Methods Fluids"},{"key":"115_CR14","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.cma.2009.09.029","volume":"199","author":"PW Hsieh","year":"2009","unstructured":"Hsieh PW, Yang SY (2009) On efficient least-squares finite element methods for convection-dominated problems. Comput Methods Appl Mech Eng 199: 183\u2013196","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR15","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1137\/S0036142900370125","volume":"39","author":"M Majidi","year":"2001","unstructured":"Majidi M, Starke G (2001) Least-squares Galerkin methods for parabolic problems. I. Semidiscretization in time. SIAM J Numer Anal 39: 1302\u20131323","journal-title":"SIAM J Numer Anal"},{"key":"115_CR16","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1137\/S0036142900379461","volume":"39","author":"M Majidi","year":"2002","unstructured":"Majidi M, Starke G (2002) Least-squares Galerkin methods for parabolic problems. II. The fully discrete case and adaptive algorithms. SIAM J Numer Anal 39: 1648\u20131666","journal-title":"SIAM J Numer Anal"},{"key":"115_CR17","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1016\/j.cam.2008.03.030","volume":"223","author":"H Rui","year":"2009","unstructured":"Rui H, Kim SD, Kim S (2009) Split least-squares Galerkin finite element methods for linear and nonlinear parabolic problems. J Comput Appl Math 223: 938\u2013952","journal-title":"J Comput Appl Math"},{"key":"115_CR18","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0045-7825(90)90139-D","volume":"81","author":"BN Jiang","year":"1990","unstructured":"Jiang BN, Povinelli LA (1990) Least-squares finite element method for fluid dynamics. Comput Methods Appl Mech Eng 81: 13\u201337","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR19","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1002\/fld.1650170402","volume":"17","author":"LQ Tang","year":"1993","unstructured":"Tang LQ, Tsang TTH (1993) A least-square finite element method for time-dependent incompressible flows with thermal convection. Int J Numer Methods Fluids 17: 271\u2013289","journal-title":"Int J Numer Methods Fluids"},{"key":"115_CR20","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0045-7825(99)00050-X","volume":"180","author":"DP Yang","year":"1999","unstructured":"Yang DP (1999) Some least-squares Garlerkin procedures for first-order time-dependent convection\u2013diffusion system. Comput Methods Appl Mech Eng 180: 81\u201395","journal-title":"Comput Methods Appl Mech Eng"},{"key":"115_CR21","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1090\/S0025-5718-99-01172-2","volume":"69","author":"DP Yang","year":"2000","unstructured":"Yang DP (2000) Analysis of least-squares mixed finite element methods for nonlinear nonstationay convection\u2013diffusion problems. Math Comput 69: 929\u2013963","journal-title":"Math Comput"},{"key":"115_CR22","first-page":"153","volume":"20","author":"DP Yang","year":"2002","unstructured":"Yang DP (2002) Least-squares mixed finite element methods for non-linear parabolic problems. J Comput Math 20: 153\u2013164","journal-title":"J Comput Math"},{"key":"115_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1990-1023042-6","volume":"55","author":"JH Bramble","year":"1990","unstructured":"Bramble JH, Pasciak JE, Xu J (1990) Parallel multilevel preconditioners. Math Comput 55: 1\u201322","journal-title":"Math Comput"},{"key":"115_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1991-1090464-8","volume":"57","author":"JH Bramble","year":"1991","unstructured":"Bramble JH, Pasciak JE, Xu J (1991) Convergence estimates for product iterative methods with application to domain decomposition. Math Comput 57: 1\u201321","journal-title":"Math Comput"},{"key":"115_CR25","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1137\/0915039","volume":"15","author":"XC Cai","year":"1994","unstructured":"Cai XC (1994) Some domain decomposition algorithms for nonselfadjont elliptic and parabolic partial differential equations. SIAM J Sci Comput 15: 587\u2013603","journal-title":"SIAM J Sci Comput"},{"key":"115_CR26","unstructured":"Dryja M, Widlund OB (1987) An additive variant of Schwarz alternating methods for many subregions, T ech Report 339 Dept of Comp Sci Coutant Institute"},{"key":"115_CR27","first-page":"74","volume":"9","author":"T Lu","year":"1991","unstructured":"Lu T, Shih TM, Liem CB (1991) Two synchronous parallel algorithms for partial differential equations. J Comput Math 9: 74\u201385","journal-title":"J Comput Math"},{"key":"115_CR28","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0377-0427(00)00518-5","volume":"128","author":"J Xu","year":"2001","unstructured":"Xu J (2001) The method of subspace corrections. J Comput Appl Math 128: 335\u2013362","journal-title":"J Comput Appl Math"},{"key":"115_CR29","unstructured":"Xu J (1989) Theory of multilevel methods. PhD thesis, Cornell University"},{"key":"115_CR30","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1137\/1034116","volume":"34","author":"J Xu","year":"1992","unstructured":"Xu J (1992) Iterative methods by space decomposition and subspace correction: a unifying approach. SIAM Rev 34: 581\u2013613","journal-title":"SIAM Rev"},{"key":"115_CR31","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF01385713","volume":"60","author":"XC Cai","year":"1991","unstructured":"Cai XC (1991) Additive Schwarz algorithms for parabolic convection\u2013diffusion equations. Numer Math 60: 41\u201361","journal-title":"Numer Math"},{"key":"115_CR32","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1137\/0915039","volume":"15","author":"XC Cai","year":"1994","unstructured":"Cai XC (1994) Multiplicative Schwarz methods for parabolic problem. SIAM J Sci Comput 15: 587\u2013603","journal-title":"SIAM J Sci Comput"},{"key":"115_CR33","first-page":"24","volume":"14","author":"XC Tai","year":"1998","unstructured":"Tai XC (1998) A space decomposition method for parabolic equations. Numer Methods Partial Differ Equ 14: 24\u201346","journal-title":"Numer Methods Partial Differ Equ"},{"key":"115_CR34","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1007\/BF02677411","volume":"14","author":"H Rui","year":"1998","unstructured":"Rui H, Yang DP (1998) Schwarz type domain decomposition algorithms for parabolic equations and error estimates. Acta Math Appl Sinica 14: 300\u2013313","journal-title":"Acta Math Appl Sinica"},{"key":"115_CR35","first-page":"501","volume":"19","author":"H Rui","year":"2001","unstructured":"Rui H, Yang DP (2001) Multiplicative Schwarz algorithm with time stepping along characteristics for convection diffusion equations. J Comput Math 19: 501\u2013510","journal-title":"J Comput Math"},{"key":"115_CR36","volume-title":"Sobolev spaces","author":"RA Adams","year":"1975","unstructured":"Adams RA (1975) Sobolev spaces. Academic Press, New York"},{"key":"115_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/b137868","volume-title":"Domain decomposition methods\u2014algorithms and theory","author":"A Toselli","year":"2005","unstructured":"Toselli A, Widlund O (2005) Domain decomposition methods\u2014algorithms and theory. Springer, Berlin"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-010-0115-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00607-010-0115-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-010-0115-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T21:46:59Z","timestamp":1559425619000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00607-010-0115-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,19]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["115"],"URL":"https:\/\/doi.org\/10.1007\/s00607-010-0115-y","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,19]]}}}