{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T04:03:34Z","timestamp":1769573014621,"version":"3.49.0"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T00:00:00Z","timestamp":1548720000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov? Agentura ?esk? Republiky","doi-asserted-by":"publisher","award":["16-03230S"],"award-info":[{"award-number":["16-03230S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s10444-019-09662-4","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T02:26:18Z","timestamp":1548728778000},"page":"1853-1862","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On error indicators for optimizing parameters in stabilized methods"],"prefix":"10.1007","volume":"45","author":[{"given":"Petr","family":"Knobloch","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4638-0697","authenticated-orcid":false,"given":"Petr","family":"Luk\u00e1\u0161","sequence":"additional","affiliation":[]},{"given":"Pavel","family":"Solin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,29]]},"reference":[{"key":"9662_CR1","volume-title":"Robust Numerical Methods for Singularly Perturbed Differential Equations. Convection\u2013Diffusion\u2013Reaction and Flow Problems, 2nd edn","author":"H-G Roos","year":"2008","unstructured":"Roos, H.-G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations. Convection\u2013Diffusion\u2013Reaction and Flow Problems, 2nd edn. Springer, Berlin (2008)"},{"key":"9662_CR2","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1016\/j.cma.2007.12.019","volume":"197","author":"V John","year":"2008","unstructured":"John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection\u2013diffusion equations: Part II \u2013 Analysis for P 1 and Q 1 finite elements. Comput. Methods Appl. Mech. Eng. 197, 1997\u20132014 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9662_CR3","doi-asserted-by":"publisher","first-page":"2916","DOI":"10.1016\/j.cma.2011.04.016","volume":"200","author":"V John","year":"2011","unstructured":"John, V., Knobloch, P., Savescu, S.B.: A posteriori optimization of parameters in stabilized methods for convection\u2013diffusion problems - Part I. Comput. Methods Appl. Mech. Eng. 200, 2916\u20132929 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9662_CR4","doi-asserted-by":"crossref","unstructured":"John, V., Knobloch, P.: Adaptive computation of parameters in stabilized methods for convection\u2013diffusion problems. In: Cangiani, A., Davidchack, R.L., Georgoulis, E.H., Gorban, A., Levesley, J., Tretyakov, M.V. (eds.) Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011, pp 275\u2013283. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-33134-3_30"},{"key":"9662_CR5","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/j.amc.2014.12.084","volume":"267","author":"P Luk\u00e1\u0161","year":"2015","unstructured":"Luk\u00e1\u0161, P.: Optimization of parameters in SDFEM for different spaces of parameters. Appl. Math. Comput. 267, 711\u2013715 (2015)","journal-title":"Appl. Math. Comput."},{"key":"9662_CR6","doi-asserted-by":"crossref","unstructured":"Luk\u00e1\u0161, P.: A posteriori optimization of parameters in the SUPG method for higher degree FE spaces. In: Knobloch, P. (ed.) Boundary and Interior Layers, Computational and Asymptotic Methods \u2013 BAIL 2014, Lect. Notes Comput. Sci. Eng., vol. 108, pp 171\u2013182. Springer (2015)","DOI":"10.1007\/978-3-319-25727-3_13"},{"key":"9662_CR7","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.amc.2017.01.034","volume":"319","author":"P Luk\u00e1\u0161","year":"2018","unstructured":"Luk\u00e1\u0161, P., Knobloch, P.: Adaptive techniques in SOLD methods. Appl. Math. Comput. 319, 24\u201330 (2018)","journal-title":"Appl. Math. Comput."},{"key":"9662_CR8","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1142\/S0218202503003057","volume":"13","author":"C Bernardi","year":"2003","unstructured":"Bernardi, C., Girault, V., Hecht, F.: A posteriori analysis of a penalty method and application to the Stokes problem. Math. Models Methods Appl. Sci. 13, 1599\u20131628 (2003)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"9662_CR9","doi-asserted-by":"publisher","first-page":"1585","DOI":"10.1137\/110837796","volume":"51","author":"M Ainsworth","year":"2013","unstructured":"Ainsworth, M., Allendes, A., Barrenechea, G.R., Rankin, R.: On the adaptive selection of the parameter in stabilized finite element approximations. SIAM J. Numer. Anal. 51, 1585\u20131609 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"9662_CR10","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0045-7825(94)90139-2","volume":"111","author":"D Silvester","year":"1994","unstructured":"Silvester, D.: Optimal low order finite element methods for incompressible flow. Comput. Methods Appl. Mech. Eng. 111, 357\u2013368 (1994)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9662_CR11","volume-title":"The Finite Element Method for Elliptic Problems","author":"PG Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, New York (1978)"},{"key":"9662_CR12","doi-asserted-by":"crossref","DOI":"10.1002\/0471764108","volume-title":"Partial Differential Equations and the Finite Element Method","author":"P \u0160ol\u00edn","year":"2005","unstructured":"\u0160ol\u00edn, P.: Partial Differential Equations and the Finite Element Method. Wiley, Hoboken (2005)"},{"key":"9662_CR13","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0045-7825(82)90071-8","volume":"32","author":"AN Brooks","year":"1982","unstructured":"Brooks, A.N., Hughes, T.J.R.: Streamline upwind\/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199\u2013259 (1982)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9662_CR14","doi-asserted-by":"publisher","first-page":"2197","DOI":"10.1016\/j.cma.2006.11.013","volume":"196","author":"V John","year":"2007","unstructured":"John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection\u2013diffusion equations: Part I \u2013 A review. Comput. Methods Appl. Mech. Eng. 196, 2197\u20132215 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9662_CR15","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1023\/A:1011430410075","volume":"65","author":"MB Giles","year":"2000","unstructured":"Giles, M.B., Pierce, N.A.: An introduction to the adjoint approach to design. Flow Turbul Combust 65, 393\u2013415 (2000)","journal-title":"Flow Turbul Combust"},{"key":"9662_CR16","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)"},{"issue":"100","key":"9662_CR17","doi-asserted-by":"publisher","first-page":"9","DOI":"10.11588\/ans.2015.100.20553","volume":"3","author":"MS Aln\u00e6s","year":"2015","unstructured":"Aln\u00e6s, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, Ch., Ring, J., Rognes, M.E., Wells, G.N.: The FEniCS project version 1.5. Archive of Numerical Software 3(100), 9\u201323 (2015). https:\/\/doi.org\/10.11588\/ans.2015.100.20553","journal-title":"Archive of Numerical Software"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09662-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09662-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09662-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T02:06:24Z","timestamp":1662861984000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09662-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,29]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["9662"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09662-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,29]]},"assertion":[{"value":"17 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}