{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T23:40:25Z","timestamp":1680306025147},"reference-count":46,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as an operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyze the properties of the Rothe method concerning stability and convergence for this kind of systems. We consider a regularization of the operator DAE and prove the weak convergence of the implicit Euler scheme. Furthermore, we consider perturbations in the semi-discrete systems which correspond to additional errors such as spatial discretization errors.<\/jats:p>","DOI":"10.1515\/cmam-2017-0003","type":"journal-article","created":{"date-parts":[[2017,4,14]],"date-time":"2017-04-14T10:01:05Z","timestamp":1492164065000},"page":"533-552","source":"Crossref","is-referenced-by-count":0,"title":["Convergence of the Rothe Method Applied to Operator DAEs Arising in Elastodynamics"],"prefix":"10.1515","volume":"17","author":[{"given":"Robert","family":"Altmann","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik MA4-5 , Technische Universit\u00e4t Berlin , Str. des 17. Juni 136, 10623 Berlin , Germany"}]}],"member":"374","published-online":{"date-parts":[[2017,4,14]]},"reference":[{"key":"2023033116270844465_j_cmam-2017-0003_ref_001_w2aab3b7b3b1b6b1ab1b5b1Aa","unstructured":"R. A.  Adams and J. J. F.  Fournier,\nSobolev Spaces, 2nd ed.,\nElsevier, Amsterdam, 2003."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_002_w2aab3b7b3b1b6b1ab1b5b2Aa","doi-asserted-by":"crossref","unstructured":"R.  Altmann,\nIndex reduction for operator differential-algebraic equations in elastodynamics,\nZAMM Z. Angew. Math. Mech. 93 (2013), no. 9, 648\u2013664.\n10.1002\/zamm.201200125","DOI":"10.1002\/zamm.201200125"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_003_w2aab3b7b3b1b6b1ab1b5b3Aa","unstructured":"R.  Altmann,\nRegularization and simulation of constrained partial differential equations\nPh.D. thesis, Technische Universit\u00e4t Berlin, 2015."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_004_w2aab3b7b3b1b6b1ab1b5b4Aa","doi-asserted-by":"crossref","unstructured":"R.  Altmann and J.  Heiland,\nFinite element decomposition and minimal extension for flow equations,\nESAIM Math. Model. Numer. Anal. 49 (2015), no. 5, 1489\u20131509.\n10.1051\/m2an\/2015029","DOI":"10.1051\/m2an\/2015029"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_005_w2aab3b7b3b1b6b1ab1b5b5Aa","unstructured":"M.  Arnold,\nZur Theorie und zur numerischen L\u00f6sung von Anfangswertproblemen f\u00fcr differentiell-algebraische Systeme von h\u00f6herem Index,\nVDI, D\u00fcsseldorf, 1998."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_006_w2aab3b7b3b1b6b1ab1b5b6Aa","doi-asserted-by":"crossref","unstructured":"M.  Arnold and O.  Br\u00fcls,\nConvergence of the generalized-\u03b1 scheme for constrained mechanical systems,\nMultibody Syst. Dyn. 18 (2007), no. 2, 185\u2013202.\n10.1007\/s11044-007-9084-0","DOI":"10.1007\/s11044-007-9084-0"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_007_w2aab3b7b3b1b6b1ab1b5b7Aa","doi-asserted-by":"crossref","unstructured":"O. A.  Bauchau,\nFlexible Multibody Dynamics,\nSolid Mech. 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Math. 15 (2015), no. 6, 1653\u20131701.\n10.1007\/s10208-014-9238-4","DOI":"10.1007\/s10208-014-9238-4"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_017_w2aab3b7b3b1b6b1ab1b5c17Aa","doi-asserted-by":"crossref","unstructured":"E.  Emmrich and M.  Thalhammer,\nConvergence of a time discretisation for doubly nonlinear evolution equations of second order,\nFound. Comput. Math. 10 (2010), no. 2, 171\u2013190.\n10.1007\/s10208-010-9061-5","DOI":"10.1007\/s10208-010-9061-5"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_018_w2aab3b7b3b1b6b1ab1b5c18Aa","doi-asserted-by":"crossref","unstructured":"E.  Emmrich and M.  Thalhammer,\nStiffly accurate Runge\u2013Kutta methods for nonlinear evolution problems governed by a monotone operator,\nMath. Comp. 79 (2010), no. 270, 785\u2013806.","DOI":"10.1090\/S0025-5718-09-02285-6"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_019_w2aab3b7b3b1b6b1ab1b5c19Aa","doi-asserted-by":"crossref","unstructured":"E.  Emmrich and M.  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Mehrmann,\nDifferential-Algebraic Equations: Analysis and Numerical Solution,\nEuropean Mathematical Society, Z\u00fcrich, 2006.","DOI":"10.4171\/017"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_026_w2aab3b7b3b1b6b1ab1b5c26Aa","doi-asserted-by":"crossref","unstructured":"R.  Lamour, R.  M\u00e4rz and C.  Tischendorf,\nDifferential-Algebraic Equations: A Projector Based Analysis,\nSpringer, Heidelberg, 2013.","DOI":"10.1007\/978-3-642-27555-5"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_027_w2aab3b7b3b1b6b1ab1b5c27Aa","unstructured":"J.  Lennart and M.  Matthes,\nNumerical analysis of nonlinear PDAEs: A coupled systems approach and its application to circuit simulation,\npreprint (2013), https:\/\/www.mathematik.hu-berlin.de\/de\/forschung\/pub\/pub-2013."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_028_w2aab3b7b3b1b6b1ab1b5c28Aa","doi-asserted-by":"crossref","unstructured":"P.  L\u00f6tstedt and L. R.  Petzold,\nNumerical solution of nonlinear differential equations with algebraic constraints. I. Convergence results for backward differentiation formulas,\nMath. Comp. 46 (1986), no. 174, 491\u2013516.","DOI":"10.1090\/S0025-5718-1986-0829621-X"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_029_w2aab3b7b3b1b6b1ab1b5c29Aa","doi-asserted-by":"crossref","unstructured":"C.  Lunk and B.  Simeon,\nThe reverse method of lines in flexible multibody dynamics,\nMultibody Dynamics,\nComput. Methods Appl. Sci. 12,\nSpringer, Berlin (2009), 95\u2013118.","DOI":"10.1007\/978-1-4020-8829-2_6"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_030_w2aab3b7b3b1b6b1ab1b5c30Aa","doi-asserted-by":"crossref","unstructured":"V.  Mehrmann,\nIndex concepts for differential-algebraic equations,\nEncyclopedia of Applied and Computational Mathematics,\nSpringer, Berlin (2015), 676\u2013681.","DOI":"10.1007\/978-3-540-70529-1_120"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_031_w2aab3b7b3b1b6b1ab1b5c31Aa","unstructured":"N. M.  Newmark,\nA method of computation for structural dynamics,\nProc. Amer. Soc. Civil Eng. 3 (1959), http:\/\/ci.nii.ac.jp\/naid\/10005333341\/en\/."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_032_w2aab3b7b3b1b6b1ab1b5c32Aa","unstructured":"M.  Renardy and R. C.  Rogers,\nAn Introduction to Partial Differential Equations, 2nd ed.,\nSpringer, New York, 2004."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_033_w2aab3b7b3b1b6b1ab1b5c33Aa","doi-asserted-by":"crossref","unstructured":"R.  Riaza,\nDifferential-Algebraic Systems,\nWorld Scientific, Hackensack, 2008.","DOI":"10.1142\/6746"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_034_w2aab3b7b3b1b6b1ab1b5c34Aa","unstructured":"T.  Roub\u00ed\u010dek,\nNonlinear Partial Differential Equations with Applications,\nBirkh\u00e4user, Basel, 2005."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_035_w2aab3b7b3b1b6b1ab1b5c35Aa","doi-asserted-by":"crossref","unstructured":"W.  Schiehlen, N.  Guse and R.  Seifried,\nMultibody dynamics in computational mechanics and engineering applications,\nComput. Methods Appl. Mech. Engrg. 195 (2006), no. 41\u201343, 5509\u20135522.\n10.1016\/j.cma.2005.04.024","DOI":"10.1016\/j.cma.2005.04.024"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_036_w2aab3b7b3b1b6b1ab1b5c36Aa","doi-asserted-by":"crossref","unstructured":"A. A.  Shabana,\nFlexible multibody dynamics: Review of past and recent developments,\nMultibody Syst. Dyn. 1 (1997), no. 2, 189\u2013222.\n10.1023\/A:1009773505418","DOI":"10.1023\/A:1009773505418"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_037_w2aab3b7b3b1b6b1ab1b5c37Aa","doi-asserted-by":"crossref","unstructured":"B.  Simeon,\nDAEs and PDEs in elastic multibody systems,\nNumer. Algorithms 19 (1998), 235\u2013246.\n10.1023\/A:1019118809892","DOI":"10.1023\/A:1019118809892"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_038_w2aab3b7b3b1b6b1ab1b5c38Aa","unstructured":"B.  Simeon,\nNumerische Simulation Gekoppelter Systeme von Partiellen und Differential-algebraischen Gleichungen der Mehrk\u00f6rperdynamik,\nVDI, D\u00fcsseldorf, 2000."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_039_w2aab3b7b3b1b6b1ab1b5c39Aa","doi-asserted-by":"crossref","unstructured":"B.  Simeon,\nOn Lagrange multipliers in flexible multibody dynamics,\nComput. Methods Appl. Mech. Engrg. 195 (2006), no. 50\u201351, 6993\u20137005.\n10.1016\/j.cma.2005.04.015","DOI":"10.1016\/j.cma.2005.04.015"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_040_w2aab3b7b3b1b6b1ab1b5c40Aa","doi-asserted-by":"crossref","unstructured":"B.  Simeon,\nComputational Flexible Multibody Dynamics. A Differential-Algebraic Approach,\nDiffer.-Algebr. Equ. Forum,\nSpringer, Berlin, 2013.","DOI":"10.1007\/978-3-642-35158-7"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_041_w2aab3b7b3b1b6b1ab1b5c41Aa","unstructured":"R.  Temam,\nNavier\u2013Stokes Equations. Theory and Numerical Analysis,\nNorth-Holland, Amsterdam, 1977."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_042_w2aab3b7b3b1b6b1ab1b5c42Aa","unstructured":"C.  Tischendorf,\nCoupled systems of differential algebraic and partial differential equations in circuit and device simulation. Modeling and numerical analysis,\nHabilitationsschrift, Humboldt-Universit\u00e4t zu Berlin, 2003."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_043_w2aab3b7b3b1b6b1ab1b5c43Aa","doi-asserted-by":"crossref","unstructured":"F.  Tr\u00f6ltzsch,\nOptimale Steuerung partieller Differentialgleichungen: Theorie, Verfahren und Anwendungen,\nVieweg & Teubner, Wiesbaden, 2009.","DOI":"10.1007\/978-3-8348-9357-4"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_044_w2aab3b7b3b1b6b1ab1b5c44Aa","unstructured":"E. L.  Wilson,\nThree Dimensional Static and Dynamic Analysis of Structures: A Physical Approach with Emphasis on Earthquake Engineering,\nComputers and Structures, Berkeley, 1998."},{"key":"2023033116270844465_j_cmam-2017-0003_ref_045_w2aab3b7b3b1b6b1ab1b5c45Aa","doi-asserted-by":"crossref","unstructured":"J.  Wloka,\nPartial Differential Equations,\nCambridge University Press, Cambridge, 1987.","DOI":"10.1017\/CBO9781139171755"},{"key":"2023033116270844465_j_cmam-2017-0003_ref_046_w2aab3b7b3b1b6b1ab1b5c46Aa","doi-asserted-by":"crossref","unstructured":"E.  Zeidler,\nNonlinear Functional Analysis and its Applications IIa: Linear Monotone Operators,\nSpringer, New York, 1990.","DOI":"10.1007\/978-1-4612-0981-2"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/17\/4\/article-p533.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0003\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T23:04:28Z","timestamp":1680303868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2017-0003\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,14]]},"references-count":46,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,9,9]]},"published-print":{"date-parts":[[2017,10,1]]}},"alternative-id":["10.1515\/cmam-2017-0003"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2017-0003","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2017,4,14]]}}}