{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T21:14:09Z","timestamp":1778188449284,"version":"3.51.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput. Visual Sci."],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s00791-014-0221-z","type":"journal-article","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T05:01:09Z","timestamp":1410757269000},"page":"15-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On the robustness and optimality of algebraic multilevel methods for reaction\u2013diffusion type problems"],"prefix":"10.1007","volume":"16","author":[{"given":"Johannes","family":"Kraus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monika","family":"Wolfmayr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,9,16]]},"reference":[{"key":"221_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511624100","volume-title":"Iterative Solution Methods","author":"O Axelsson","year":"1994","unstructured":"Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)"},{"key":"221_CR2","volume-title":"Finite Element Solution of Boundary Value Problems: Theory and Computations","author":"O Axelsson","year":"1984","unstructured":"Axelsson, O., Barker, V.: Finite Element Solution of Boundary Value Problems: Theory and Computations. Academic Press, Orlando (1984)"},{"key":"221_CR3","unstructured":"Axelsson, O., Blaheta, R.: Two simple derivations of universal bounds for the C.B.S. inequality constant. Appl. Math. 49(1), 57\u201372 (2004)"},{"issue":"5","key":"221_CR4","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1137\/S1064827597320058","volume":"20","author":"O Axelsson","year":"1999","unstructured":"Axelsson, O., Padiy, A.: On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems. SIAM J. Sci. Comput. 20(5), 1807\u20131830 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"221_CR5","doi-asserted-by":"crossref","unstructured":"Axelsson, O., Vassilevski, P.: Algebraic multilevel preconditioning methods. I. Numer. Math. 56(2\u20133), 157\u2013177 (1989)","DOI":"10.1007\/BF01409783"},{"key":"221_CR6","unstructured":"Axelsson, O., Vassilevski, P.: Algebraic multilevel preconditioning methods. II. SIAM J. Numer. Anal. 27(6), 1569\u20131590 (1990)"},{"issue":"1","key":"221_CR7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1002\/nla.1680010108","volume":"1","author":"O Axelsson","year":"1994","unstructured":"Axelsson, O., Vassilevski, P.: Variable-step multilevel preconditioning methods, I: self-adjoint and positive definite elliptic problems. Numer. Linear Algebra Appl. 1(1), 75\u2013101 (1994)","journal-title":"Numer. Linear Algebra Appl."},{"key":"221_CR8","unstructured":"Axelsson, O., Vassilevski, P.: The AMLI Method: An Algebraic Multilevel Iteration Method for Positive Definite Sparse Matrices. University of Nijmegen, Departement of Mathematics (1999)"},{"key":"221_CR9","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. Republished by SIAM in April 2002","DOI":"10.1137\/1.9780898719208"},{"key":"221_CR10","doi-asserted-by":"crossref","unstructured":"Collins, G.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Automata theory and formal languages (Second GI Conf., Kaiserslautern, 1975). Lecture Notes in Comput. Sci., vol. 33, pp. 134\u2013183 (1975)","DOI":"10.1007\/3-540-07407-4_17"},{"key":"221_CR11","unstructured":"Collins, G., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. J. Symb. Comput. 12(3), 299\u2013328 (1991)"},{"issue":"B65a","key":"221_CR12","first-page":"1","volume":"65","author":"M Kauers","year":"2011","unstructured":"Kauers, M.: How to use cylindrical algebraic decomposition. Semin. Lothar. Comb. 65(B65a), 1\u201316 (2011)","journal-title":"Semin. Lothar. Comb."},{"key":"221_CR13","doi-asserted-by":"crossref","unstructured":"Kollmann, M., Kolmbauer, M.: A preconditioned MinRes solver for time-periodic parabolic optimal control problems. Numer. Linear Algebra Appl. 20(5), 761\u2013784 (2013)","DOI":"10.1002\/nla.1842"},{"issue":"3","key":"221_CR14","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.camwa.2012.06.012","volume":"65","author":"M Kollmann","year":"2013","unstructured":"Kollmann, M., Kolmbauer, M., Langer, U., Wolfmayr, M., Zulehner, W.: A finite element solver for a multiharmonic parabolic optimal control problem. Comput. Math. Appl. 65(3), 469\u2013486 (2013)","journal-title":"Comput. Math. Appl."},{"issue":"8","key":"221_CR15","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1002\/nla.281","volume":"9","author":"J Kraus","year":"2002","unstructured":"Kraus, J.: An algebraic preconditioning method for M-matrices: linear versus non-linear multilevel iteration. Numer. Linear Algebra Appl. 9(8), 599\u2013618 (2002)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"6","key":"221_CR16","doi-asserted-by":"crossref","first-page":"A2872","DOI":"10.1137\/110845082","volume":"34","author":"J Kraus","year":"2012","unstructured":"Kraus, J.: Additive Schur complement approximation and application to multilevel preconditioning. SIAM J. Sci. Comput. 34(6), A2872\u2013A2895 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"221_CR17","doi-asserted-by":"crossref","unstructured":"Kraus, J., Lymbery, M., Margenov, S.: Robust multilevel methods for quadratic finite element anisotropic elliptic problems. Numer. Linear Algebra Appl. 21(3), 375\u2013398 (2014)","DOI":"10.1002\/nla.1876"},{"key":"221_CR18","doi-asserted-by":"crossref","DOI":"10.1515\/9783110214833","volume-title":"Robust Algebraic Multilevel Methods and Algorithms, Volume 5 of Radon Series on Computational and Applied Mathematics","author":"J Kraus","year":"2009","unstructured":"Kraus, J., Margenov, S.: Robust Algebraic Multilevel Methods and Algorithms, Volume 5 of Radon Series on Computational and Applied Mathematics. De Gruyter, Berlin (2009)"},{"issue":"1","key":"221_CR19","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1002\/pamm.201210332","volume":"12","author":"U Langer","year":"2012","unstructured":"Langer, U., Wolfmayr, M.: Multiharmonic finite element solvers for time-periodic parabolic optimal control problems. Proc. Appl. Math. Mech. (PAMM) 12(1), 687\u2013688 (2012)","journal-title":"Proc. Appl. Math. Mech. (PAMM)"},{"key":"221_CR20","unstructured":"Langer, U., Wolfmayr, M.: Multiharmonic finite element analysis of a time-periodic parabolic optimal control problem. J. Numer. Math. 21(4), 265\u2013300 (2013)"},{"key":"221_CR21","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.jco.2006.10.003","volume":"4\u20136","author":"R Lazarov","year":"2007","unstructured":"Lazarov, R., Margenov, S.: CBS constants for graph-Laplacians and application to multilevel methods for discontinuous Galerkin systems. J. Complex. 4\u20136, 498\u2013515 (2007)","journal-title":"J. Complex."},{"key":"221_CR22","unstructured":"Lymbery, M., Margenov, S.: Robust semi-coarsening multilevel preconditioning of biquadratic fem systems. Cent. Eur. J. Math. 10(1), 357\u2013369 (2012)"},{"key":"221_CR23","doi-asserted-by":"crossref","unstructured":"Maitre, J., Musy, F.: The contraction number of a class of two-level methods: an exact evaluation for some finite element subspaces and model problems. Lect. Notes Math. 960, 535\u2013544 (1982)","DOI":"10.1007\/BFb0069942"},{"key":"221_CR24","first-page":"323","volume":"30","author":"C Mense","year":"2008","unstructured":"Mense, C., Nabben, R.: On algebraic multilevel methods for non-symmetric systems\u2014convergence results. Electron. Trans. Numer. Anal. 30, 323\u2013345 (2008)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"5","key":"221_CR25","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1002\/nla.542","volume":"15","author":"Y Notay","year":"2008","unstructured":"Notay, Y., Vassilevski, P.: Recursive Krylov-based multigrid cycles. Numer. Linear Algebra Appl. 15(5), 473\u2013487 (2008)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"221_CR26","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1137\/0712047","volume":"12","author":"C Paige","year":"1975","unstructured":"Paige, C., Saunders, M.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12(4), 617\u2013629 (1975)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Computing and Visualization in Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-014-0221-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00791-014-0221-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-014-0221-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T23:53:43Z","timestamp":1565826823000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00791-014-0221-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["221"],"URL":"https:\/\/doi.org\/10.1007\/s00791-014-0221-z","relation":{},"ISSN":["1432-9360","1433-0369"],"issn-type":[{"value":"1432-9360","type":"print"},{"value":"1433-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}