{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:02:24Z","timestamp":1776769344917,"version":"3.51.2"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1996,3,1]],"date-time":"1996-03-01T00:00:00Z","timestamp":825638400000},"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":[[1996,3]]},"DOI":"10.1007\/bf02238356","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T17:42:35Z","timestamp":1131990155000},"page":"25-48","source":"Crossref","is-referenced-by-count":9,"title":["Multilevel preconditioned augmented Lagrangian techniques for 2nd order mixed problems","L\u00f6sung gemischter Probleme zweiter Ordnung mit Multilevel-Vorkonditionierung und erweiteter Lagrange-Multiplikatoren-Technik"],"prefix":"10.1007","volume":"57","author":[{"given":"R.","family":"Hiptmair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Schiekofer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Wohlmuth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02238356_CR1","series-title":"User's Guide 6.0","volume-title":"PLTMG: A software package for solving elliptic partial differential equations","author":"R. Bank","year":"1990","unstructured":"Bank, R.: PLTMG: A software package for solving elliptic partial differential equations, User's Guide 6.0. Philadelphia: SIAM 1990."},{"key":"BF02238356_CR2","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1007\/BF01405194","volume":"56","author":"R. Bank","year":"1990","unstructured":"Bank, R., Welfert, B., Yseretant, H.: A class of iterative methods for solving saddle point problems. Numer. Math56, 645\u2013666 (1990).","journal-title":"Numer. Math"},{"key":"BF02238356_CR3","unstructured":"Bornemann, F.: A sharpened condition number estimate for the BPX-preconditioner of elliptic finite element problems on highly nonuniform triangulations. Preprint SC 91-9 ZIB Berlin (1991)."},{"key":"BF02238356_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1990-1023042-6","volume":"55","author":"J. H. Bramble","year":"1990","unstructured":"Bramble, J. H., Pasciak, J. E., Xu, J.: Parallel multilevel preconditioners. Math. Comp.55, 1\u201322 (1990).","journal-title":"Math. Comp."},{"key":"BF02238356_CR5","first-page":"129","volume":"57","author":"F. Brezzi","year":"1974","unstructured":"Brezzi, F.: On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers. Math. Comp.57, 129\u2013151 (1974).","journal-title":"Math. Comp."},{"key":"BF02238356_CR6","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1137\/0729042","volume":"29","author":"S. Brenner","year":"1992","unstructured":"Brenner, S.: A multigrid algorithm for the lowest order Raviart-Thomas mixed triangular finite element method. SIAM J. Numer. Anal.29, 647\u2013678 (1992).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02238356_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-07234-9","volume-title":"Finite Elemente","author":"D. Braess","year":"1992","unstructured":"Braess, D.: Finite Elemente. Berlin Heidelberg New York Tokyo: Springer 1992."},{"key":"BF02238356_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and hybrid finite element methods","author":"F. Brezzi","year":"1991","unstructured":"Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. New York: Springer 1991."},{"key":"BF02238356_CR9","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1137\/0914065","volume":"14","author":"Z. Cai","year":"1993","unstructured":"Cai, Z., Goldstein, C. I., Pasciak, J.: Multilevel, iteration for mixed finite element systems with penalty. SIAM J. Sci. Comput.14, 1072\u20131088 (1993).","journal-title":"SIAM J. Sci. Comput."},{"key":"BF02238356_CR10","volume-title":"The finite element method for elliptic problems","author":"P. Ciarlet","year":"1987","unstructured":"Ciarlet, P.: The finite element method for elliptic problems. Amsterdam: North-Holland 1987."},{"key":"BF02238356_CR11","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01385864","volume":"63","author":"W. Dahmen","year":"1992","unstructured":"Dahmen, W., Kunoth, A.: Multilevel preconditioning, Numer. Math.63, 315\u2013344 (1992).","journal-title":"Numer. Math."},{"key":"BF02238356_CR12","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0899-8248(89)90018-9","volume":"1","author":"P. Deuflhard","year":"1989","unstructured":"Deuflhard, P., Leinen, P., Yserentant, H.: Concepts of an adaptive hierarchical finite element code. IMPACT Comput. Sci. Eng.1, 3\u201335 (1989).","journal-title":"IMPACT Comput. Sci. Eng."},{"key":"BF02238356_CR13","series-title":"Lecture Notes in Mathematics","volume-title":"Preconditioning indefinite systems arising from mixed finite element discretization of second order elliptic problems","author":"R. Ewing","year":"1990","unstructured":"Ewing, R., Lazarov, D., Lu, P., Vassilevski, P.: Preconditioning indefinite systems arising from mixed finite element discretization of second order elliptic problems. Berlin Heidelberg New York Tokyo: Springer 1990 (Lecture Notes in Mathematics, Vol. 1957)."},{"key":"BF02238356_CR14","first-page":"739","volume":"26","author":"J. R. Ewing","year":"1992","unstructured":"Ewing, J. R., Wang, J.: Analysis of the Schwarz algorithm for mixed fiite element methods M2. AN26, 739\u2013756 (1992).","journal-title":"AN"},{"key":"BF02238356_CR15","first-page":"377","volume":"28","author":"J. R. Ewing","year":"1994","unstructured":"Ewing, J. R., Wang, J.: Analysis of multilevel decomposition iterative methods for mixed finite element methods M2. AN28, 377\u2013398 (1994).","journal-title":"AN"},{"key":"BF02238356_CR16","series-title":"Studies in Mathematics and its Applications","volume-title":"Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems","author":"M. Fortin","year":"1983","unstructured":"Fortin, M., Glowinski, R.: Augmented Lagrangian methods: Applications to the numerical solution of boundary value problems. Studies in Mathematics and its Applications, Vol. 15. Amsterdam: North-Holland 1983."},{"key":"BF02238356_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite element methods for Navier-Stokes equations: theory and algorithms","author":"V. Girault","year":"1986","unstructured":"Girault, V., Raviart, P. A.: Finite element methods for Navier-Stokes equations: theory and algorithms. New York: Springer 1986."},{"key":"BF02238356_CR18","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970838","volume-title":"Augmented Lagrangian and operator-splitting methods in nonlinear methods in nonlinear mechanics","author":"R. Glowinski","year":"1989","unstructured":"Glowinski, R., LeTallec, P.: Augmented Lagrangian and operator-splitting methods in nonlinear methods in nonlinear mechanics. Philadelphia: SIAM 1989."},{"key":"BF02238356_CR19","unstructured":"Hiptmair, R.: Object Oriented Concepts for an Adaptive Finite Element Code, Report No. 335, Math.-Nat. Fakult\u00e4t Universit\u00e4t Augsburg (1995)."},{"key":"BF02238356_CR20","doi-asserted-by":"crossref","unstructured":"Hoppe, R. H. W., Wohlmuth, B.: Efficient Numerical Solution of Mixed Finite Element Discretizations by Adaptive Multilevel Methods, Report M9410, Mathematisches Institut, TU M\u00fcnchen 1994 (submitted to Appl. Math.).","DOI":"10.21136\/AM.1995.134292"},{"key":"BF02238356_CR21","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/BF01385762","volume":"65","author":"T. P. Mathew","year":"1993","unstructured":"Mathew, T. P.: Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, Part I: Algorithms and numerical results. Numer. Math.65, 445\u2013468 (1993).","journal-title":"Numer. Math."},{"key":"BF02238356_CR22","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01385763","volume":"65","author":"T. P. Mathew","year":"1993","unstructured":"Mathew, T. P.: Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems. Part II: Convergence theory. Numer. Math.65, 469\u2013492 (1993).","journal-title":"Numer. Math."},{"key":"BF02238356_CR23","unstructured":"Oswald, P.: Two remarks on multilevel preconditioners, Forsch.-Erg. FSU Jena, Math. \/91\/1 (1991)."},{"key":"BF02238356_CR24","series-title":"Lecture Notes in Mathematics","volume-title":"A mixed finite element method for second order elliptic problems","author":"P. A. Raviart","year":"1977","unstructured":"Raviart, P. A., Thomas, J. M.: A mixed finite element method for second order elliptic problems. Berlin Heidelberg New York: Springer 1977 (Lecture Notes in Mathematics, Vol. 606)."},{"key":"BF02238356_CR25","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1137\/0613054","volume":"13","author":"T. Rusten","year":"1992","unstructured":"Rusten, T., Winther, R.: A preconditioned iterative method for saddlepoint problems. SIAM J. Matrix Anal. Appl.13, 887\u2013904 (1992).","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"BF02238356_CR26","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/BF01385872","volume":"63","author":"P. S. Vassilevski","year":"1992","unstructured":"Vassilevski, P. S., Wang, J.: Multilevel iterative methods for mixed finite element discretizations of elliptic problems. Numer. Math.63, 503\u2013520 (1992).","journal-title":"Numer. Math."},{"key":"BF02238356_CR27","unstructured":"Wohlmuth, B.: Adaptive Multilevel-Finite-Elemente Methoden zur L\u00f6sung elliptischer Randwertprobleme. Ph.D. Thesis, Mathematisches Institut, TU M\u00fcnchen (1995)."},{"key":"BF02238356_CR28","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1137\/1034116","volume":"34","author":"J. Xu","year":"1992","unstructured":"Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev.34, 581\u2013613 (1992).","journal-title":"SIAM Rev."},{"key":"BF02238356_CR29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF01389538","volume":"49","author":"H. Yserentant","year":"1986","unstructured":"Yserentant, H.: On the multi-level splitting of finite element spaces. Numer. Math.49, 379\u2013412 (1986).","journal-title":"Numer. Math."},{"key":"BF02238356_CR30","first-page":"1","volume":"1","author":"H. Yserentant","year":"1993","unstructured":"Yserentant, H.: Old and new convergence proofs for multigrid methods. Acta Num.1, 1\u2013100 (1993).","journal-title":"Acta Num."},{"key":"BF02238356_CR31","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/BF01385873","volume":"63","author":"X. Zhang","year":"1992","unstructured":"Zhang, X.: Multilevel Schwarz methods. Numer. Math.63, 521\u2013539 (1992).","journal-title":"Numer. Math."}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02238356.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02238356\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02238356","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T11:20:30Z","timestamp":1683285630000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02238356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["BF02238356"],"URL":"https:\/\/doi.org\/10.1007\/bf02238356","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}