{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:53:33Z","timestamp":1776844413896,"version":"3.51.2"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,8,19]],"date-time":"2009-08-19T00:00:00Z","timestamp":1250640000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2009,11]]},"DOI":"10.1007\/s00211-009-0250-6","type":"journal-article","created":{"date-parts":[[2009,8,18]],"date-time":"2009-08-18T14:04:59Z","timestamp":1250604299000},"page":"63-106","source":"Crossref","is-referenced-by-count":26,"title":["A residual-based a posteriori error estimator for a two-dimensional fluid\u2013solid interaction problem"],"prefix":"10.1007","volume":"114","author":[{"given":"Gabriel N.","family":"Gatica","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George C.","family":"Hsiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salim","family":"Meddahi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,8,19]]},"reference":[{"key":"250_CR1","volume-title":"Lectures on Elliptic Boundary Value Problems","author":"S. Agmon","year":"1965","unstructured":"Agmon S.: Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton (1965)"},{"key":"250_CR2","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s002110050222","volume":"74","author":"A. Alonso","year":"1996","unstructured":"Alonso A.: Error estimators for a mixed method. Numer. Math. 74, 385\u2013395 (1996)","journal-title":"Numer. Math."},{"issue":"4","key":"250_CR3","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1137\/0719052","volume":"19","author":"D.N. Arnold","year":"1982","unstructured":"Arnold D.N.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19(4), 742\u2013760 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/BF03167064","volume":"1","author":"D.N. Arnold","year":"1984","unstructured":"Arnold D.N., Brezzi F., Douglas J.: PEERS: A new mixed finite element method for plane elasticity. Jpn. J. Appl. Math. 1, 347\u2013367 (1984)","journal-title":"Jpn. J. Appl. Math."},{"issue":"18","key":"250_CR5","doi-asserted-by":"crossref","first-page":"3443","DOI":"10.1002\/(SICI)1097-0207(19970930)40:18<3443::AID-NME221>3.0.CO;2-1","volume":"40","author":"I. Babu\u0161ka","year":"1997","unstructured":"Babu\u0161ka I., Ihlenburg F., Strouboulis T., Gangaraj S.K.: A posteriori error estimation for finite element solutions of Helmholtz\u2019 equation. Part I. The quality of local indicators and estimators. Int. J. Numer. Methods Eng. 40(18), 3443\u20133462 (1997)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"21","key":"250_CR6","doi-asserted-by":"crossref","first-page":"3883","DOI":"10.1002\/(SICI)1097-0207(19971115)40:21<3883::AID-NME231>3.0.CO;2-V","volume":"40","author":"I. Babu\u0161ka","year":"1997","unstructured":"Babu\u0161ka I., Ihlenburg F., Strouboulis T., Gangaraj S.K.: A posteriori error estimation for finite element solutions of Helmholtz\u2019 equation \u2013 Part II. Estimation of the pollution error. Int. J. Numer. Methods Eng. 40(21), 3883\u20133900 (1997)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"250_CR7","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1051\/m2an:2006036","volume":"40","author":"T. Barrios","year":"2006","unstructured":"Barrios T., Gatica G.N., Gonz\u00e1lez M., Heuer N.: A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity. ESAIM Math. Model. Numer. Anal. 40(5), 843\u2013869 (2006)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"6","key":"250_CR8","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1137\/0725070","volume":"25","author":"C. Bernardi","year":"1988","unstructured":"Bernardi C., Canuto C., Maday Y.: Generalized inf-sup conditions for Chebyshev spectral approximations of the Stokes problem. SIAM J. Numer. Anal. 25(6), 1237\u20131271 (1988)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR9","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1090\/qam\/1096235","volume":"49","author":"J. Bielak","year":"1991","unstructured":"Bielak J., MacCamy R.C.: Symmetric finite element and boundary integral coupling methods for fluid\u2013solid interaction. Q. Appl. Math. 49, 107\u2013119 (1991)","journal-title":"Q. Appl. Math."},{"issue":"7","key":"250_CR10","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1002\/(SICI)1097-0207(19990710)45:7<783::AID-NME605>3.0.CO;2-M","volume":"45","author":"Ph. Bouillard","year":"1999","unstructured":"Bouillard Ph.: Influence of the pollution on the admissible field error estimation for FE solutions of the Helmholtz equation. Int. J. Numer. Methods Eng. 45(7), 783\u2013800 (1999)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"250_CR11","doi-asserted-by":"crossref","first-page":"2431","DOI":"10.1137\/S0036142994264079","volume":"33","author":"D. Braess","year":"1996","unstructured":"Braess D., Verf\u00fcrth R.: A posteriori error estimators for the Raviart\u2013Thomas element. SIAM J. Numer. Anal. 33, 2431\u20132444 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR12","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. Springer, New York (1991)"},{"issue":"1","key":"250_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S003614290342385X","volume":"43","author":"A. Buffa","year":"2005","unstructured":"Buffa A.: Remarks on the discretization of some non-coercive operator with applications to heterogeneous Maxwell equations. SIAM J. Numer. Anal. 43(1), 1\u201318 (2005)","journal-title":"SIAM J. Numer. Anal."},{"issue":"217","key":"250_CR14","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1090\/S0025-5718-97-00790-4","volume":"66","author":"C. Carstensen","year":"1997","unstructured":"Carstensen C.: An a posteriori error estimate for a first kind integral equation. Math. Comput. 66(217), 139\u2013155 (1997)","journal-title":"Math. Comput."},{"issue":"218","key":"250_CR15","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1090\/S0025-5718-97-00837-5","volume":"66","author":"C. Carstensen","year":"1997","unstructured":"Carstensen C.: A posteriori error estimate for the mixed finite element method. Math. Comput. 66(218), 465\u2013476 (1997)","journal-title":"Math. Comput."},{"key":"250_CR16","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s002110050389","volume":"81","author":"C. Carstensen","year":"1998","unstructured":"Carstensen C., Dolzmann G.: A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81, 187\u2013209 (1998)","journal-title":"Numer. Math."},{"key":"250_CR17","volume-title":"The Finite Element Method for Elliptic Problems","author":"P.G. Ciarlet","year":"1978","unstructured":"Ciarlet P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)"},{"key":"250_CR18","first-page":"77","volume":"9","author":"P. Cl\u00e9ment","year":"1975","unstructured":"Cl\u00e9ment P.: Approximation by finite element functions using local regularisation. RAIRO Model. Math. Anal. Numer. 9, 77\u201384 (1975)","journal-title":"RAIRO Model. Math. Anal. Numer."},{"key":"250_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03537-5","volume-title":"Inverse Acoustic and Electromagnetic Scattering Theory","author":"D. Colton","year":"1998","unstructured":"Colton D., Kress R.: Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Springer, Berlin (1998)","edition":"2"},{"key":"250_CR20","first-page":"218","volume":"17","author":"G.N. Gatica","year":"2004","unstructured":"Gatica G.N.: A note on the efficiency of residual-based a-posteriori error estimators for some mixed finite element methods. Electron. Trans. Numer. Anal. 17, 218\u2013233 (2004)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"3","key":"250_CR21","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/num.20050","volume":"21","author":"G.N. Gatica","year":"2005","unstructured":"Gatica G.N., Maischak M.: A posteriori error estimates for the mixed finite element method with Lagrange multipliers. Numer. Methods Partial Differ. Equ. 21(3), 421\u2013450 (2005)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"250_CR22","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1137\/060660370","volume":"45","author":"G.N. Gatica","year":"2007","unstructured":"Gatica G.N., M\u00e1rquez A., Meddahi S.: Analysis of the coupling of primal and dual-mixed finite element methods for a two-dimensional fluid\u2013solid interaction problem. SIAM J. Numer. Anal. 45(5), 2072\u20132097 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR23","doi-asserted-by":"crossref","unstructured":"Gatica, G.N., M\u00e1rquez, A., Meddahi, S.: Analysis of the coupling of BEM, FEM, and mixed-FEM for a two-dimensional fluid\u2013solid interaction problem. Appl. Numer. Math. (2009). doi: 10.1016\/j.apnum.2008.12.025","DOI":"10.1016\/j.apnum.2008.12.025"},{"issue":"5\u20136","key":"250_CR24","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1080\/01630569908816905","volume":"20","author":"G.N. Gatica","year":"1999","unstructured":"Gatica G.N., Meddahi S.: An a-posteriori error estimate for the coupling of BEM and mixed-FEM. Numer. Funct. Anal. Optim. 20(5\u20136), 449\u2013472 (1999)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"250_CR25","unstructured":"Hsiao, G.C.: The coupling of BEM and FEM\u2014a brief review. In: Boundary Elements X, vol. 1, pp. 431\u2013445. Springer, New York (1988)"},{"key":"250_CR26","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/978-3-322-85161-1_7","volume-title":"Problems and Methods in Mathematical Physics, Teubner-Text zur Mathematik, Band 34","author":"G.C. Hsiao","year":"1994","unstructured":"Hsiao G.C.: On the boundary-field equation methods for fluid-structure interactions. In: Jentsch, L., Tr\u00f6ltzsch, F. (eds) Problems and Methods in Mathematical Physics, Teubner-Text zur Mathematik, Band 34, pp. 79\u201388. B. G. Teubner Veriagsgesellschaft, Stuttgart (1994)"},{"key":"250_CR27","first-page":"73","volume-title":"Proceedings of the Fifth International Conference on Boundary Element Technology, vol. 1","author":"G.C. Hsiao","year":"1990","unstructured":"Hsiao G.C., Kleinman R.E., Li R.-X., van der Berg P.M.: Residual error\u2014a simple and sufficient estimate of actual error in solutions of boundary integral equations. In: Grill, S., Brebbia, C.A., Cheng, A.H.-D. (eds) Proceedings of the Fifth International Conference on Boundary Element Technology, vol. 1, pp. 73\u201383. Computational Mechanics Publications, Boston (1990)"},{"key":"250_CR28","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1002\/1522-2616(200010)218:1<139::AID-MANA139>3.0.CO;2-S","volume":"218","author":"G.C. Hsiao","year":"2000","unstructured":"Hsiao G.C., Kleinman R.E., Roach G.F.: Weak solutions of fluid\u2013solid interaction problems. Math. Nachr. 218, 139\u2013163 (2000)","journal-title":"Math. Nachr."},{"key":"250_CR29","first-page":"321","volume-title":"Elastic Wave Propagation","author":"G.C. Hsiao","year":"1989","unstructured":"Hsiao G.C., Kleinman R.E., Schuetz L.S.: On variational formulations of boundary value problems for fluid\u2013solid interactions. In: McCarthy, M.F., Hayes, M.A. (eds) Elastic Wave Propagation, pp. 321\u2013326. Elsevier, North-Holland (1989)"},{"key":"250_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/b98828","volume-title":"Finite Element Analysis of Acoustic Scattering","author":"F. Ihlenburg","year":"1998","unstructured":"Ihlenburg F.: Finite Element Analysis of Acoustic Scattering. Springer, New York (1998)"},{"issue":"22","key":"250_CR31","doi-asserted-by":"crossref","first-page":"3745","DOI":"10.1002\/nme.1620382203","volume":"38","author":"F. Ihlenburg","year":"1995","unstructured":"Ihlenburg F., Babu\u0161ka I.: Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. Int. J. Numer. Methods Eng. 38(22), 3745\u20133774 (1995)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"31","key":"250_CR32","doi-asserted-by":"crossref","first-page":"4027","DOI":"10.1016\/S0045-7825(00)00314-5","volume":"190","author":"S. Irimie","year":"2001","unstructured":"Irimie S., Boiullard Ph.: A reliable a posteriori error estimator for the finite element solution of the Helmholtz equation. Comput. Methods Appl. Mech. Eng. 190(31), 4027\u20134042 (2001)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"250_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-97146-4","volume-title":"Linear Integral Equations","author":"R. Kress","year":"1989","unstructured":"Kress R.: Linear Integral Equations. Springer, Berlin (1989)"},{"issue":"4","key":"250_CR34","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1007\/s00211-004-0519-8","volume":"97","author":"M. Lonsing","year":"2004","unstructured":"Lonsing M., Verf\u00fcrth R.: A posteriori error estimators for mixed finite element methods in linear elasticity. Numer. Math. 97(4), 757\u2013778 (2004)","journal-title":"Numer. Math."},{"issue":"256","key":"250_CR35","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1090\/S0025-5718-06-01872-2","volume":"75","author":"C. Lovadina","year":"2006","unstructured":"Lovadina C., Stenberg R.: Energy norm a posteriori error estimates for mixed finite element methods. Math. Comput. 75(256), 1659\u20131674 (2006)","journal-title":"Math. Comput."},{"key":"250_CR36","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1137\/S0036142902406624","volume":"41","author":"S. Meddahi","year":"2003","unstructured":"Meddahi S., M\u00e1rquez A., Selgas V.: Computing acoustic waves in an inhomogeneous medium of the plane by a coupling of spectral and finite elements. SIAM J. Numer. Anal. 41, 1729\u20131750 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR37","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.jcp.2004.02.005","volume":"199","author":"S. Meddahi","year":"2004","unstructured":"Meddahi S., M\u00e1rquez A., Selgas V.: A new BEM-FEM coupling strategy for two-dimensional fluid\u2013solid interaction problems. J. Comput. Phys. 199, 205\u2013220 (2004)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"250_CR38","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1002\/num.20074","volume":"21","author":"S. Meddahi","year":"2005","unstructured":"Meddahi S., Sayas F.-J.: Analysis of a new BEM-FEM coupling for two dimensional fluid\u2013solid interaction. Numer. Methods Partial Differ. Equ. 21(6), 1017\u20131042 (2005)","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"3","key":"250_CR39","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1137\/050641533","volume":"45","author":"S. Repin","year":"2007","unstructured":"Repin S., Sauter S., Smolianski A.: Two-sided a posteriori error estimates for mixed formulations of elliptic problems. SIAM J. Numer. Anal. 45(3), 928\u2013945 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"250_CR40","doi-asserted-by":"crossref","unstructured":"Roberts, J.E., Thomas, J.M.: Mixed and Hybrid Methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis. Finite Element Methods (Part 1), vol. II. North-Holland, Amsterdam (1991)","DOI":"10.1016\/S1570-8659(05)80041-9"},{"key":"250_CR41","first-page":"375","volume-title":"Encyclopedia of Computational Mechanics, vol. 1","author":"E.P. Stephan","year":"2004","unstructured":"Stephan E.P.: Coupling of boundary element methods and finite element methods. In: Stein, E., Borst, R., Hughes, T.J.R. (eds) Encyclopedia of Computational Mechanics, vol. 1, pp. 375\u2013412. Wiley, New York (2004)"},{"issue":"1","key":"250_CR42","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0168-874X(95)00058-2","volume":"22","author":"J.R. Stewart","year":"1996","unstructured":"Stewart J.R., Hughes T.J.R.: A posteriori error estimation and adaptive finite element computation of the Helmholtz equation in exterior domains. Finite Elem. Anal. Des. 22(1), 15\u201324 (1996)","journal-title":"Finite Elem. Anal. Des."},{"issue":"1\u20132","key":"250_CR43","first-page":"1","volume":"25","author":"J.R. Stewart","year":"1996","unstructured":"Stewart J.R., Hughes T.J.R.: An a posteriori error estimator and hp-adaptive strategy for finite element discretizations of the Helmholtz equation in exterior domains. Finite Elem. Anal. Des. 25(1\u20132), 1\u201326 (1996)","journal-title":"Finite Elem. Anal. Des."},{"issue":"3\u20134","key":"250_CR44","first-page":"335","volume":"131","author":"J.R. Stewart","year":"1997","unstructured":"Stewart J.R., Hughes T.J.R.: Explicit residual-based a posteriori error estimation for finite element discretizations of the Helmholtz equation: Computation of the constant and new measures of error estimator quality. Comput. Methods Appl. Mech. Eng. 131(3\u20134), 335\u2013363 (1997)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"250_CR45","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0377-0427(94)90290-9","volume":"50","author":"R. Verf\u00fcrth","year":"1994","unstructured":"Verf\u00fcrth R.: A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50, 67\u201383 (1994)","journal-title":"J. Comput. Appl. Math."},{"key":"250_CR46","volume-title":"A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques","author":"R. Verf\u00fcrth","year":"1996","unstructured":"Verf\u00fcrth R.: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley, Chichester (1996)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-009-0250-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-009-0250-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-009-0250-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,9]],"date-time":"2021-10-09T20:03:20Z","timestamp":1633809800000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-009-0250-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,19]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,11]]}},"alternative-id":["250"],"URL":"https:\/\/doi.org\/10.1007\/s00211-009-0250-6","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,19]]}}}