{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T08:55:18Z","timestamp":1774601718069,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s10208-021-09498-9","type":"journal-article","created":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T22:02:30Z","timestamp":1614981750000},"page":"1739-1774","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Complexes from Complexes"],"prefix":"10.1007","volume":"21","author":[{"given":"Douglas N.","family":"Arnold","sequence":"first","affiliation":[]},{"given":"Kaibo","family":"Hu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,5]]},"reference":[{"issue":"1","key":"9498_CR1","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1137\/15M1020113","volume":"48","author":"S Amstutz","year":"2016","unstructured":"Amstutz, S., Van\u00a0Goethem, N.: Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations. SIAM Journal on Mathematical Analysis 48(1), 320\u2013348 (2016)","journal-title":"SIAM Journal on Mathematical Analysis"},{"key":"9498_CR2","doi-asserted-by":"crossref","unstructured":"Amstutz, S., Van\u00a0Goethem, N.: Incompatibility-governed elasto-plasticity for continua with dislocations. In: Proc. R. Soc. A, vol. 473, p. 20160734. The Royal Society (2017)","DOI":"10.1098\/rspa.2016.0734"},{"key":"9498_CR3","doi-asserted-by":"crossref","unstructured":"Amstutz, S., Van\u00a0Goethem, N.: The incompatibility operator: from Riemann\u2019s intrinsic view of geometry to a new model of elasto-plasticity. In: Topics in Applied Analysis and Optimisation, pp. 33\u201370. Springer (2019)","DOI":"10.1007\/978-3-030-33116-0_2"},{"issue":"1","key":"9498_CR4","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s00205-014-0806-1","volume":"216","author":"A Angoshtari","year":"2015","unstructured":"Angoshtari, A., Yavari, A.: Differential complexes in continuum mechanics. Archive for Rational Mechanics and Analysis 216(1), 193\u2013220 (2015)","journal-title":"Archive for Rational Mechanics and Analysis"},{"key":"9498_CR5","unstructured":"Arnold, D.N.: Finite element exterior calculus and applications. Lectures at Peking University, http:\/\/www-users.math.umn.edu\/~arnold\/beijing-lectures-2015\/feec-beijing-lecture5.pdf (2015)"},{"key":"9498_CR6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975543","volume-title":"Finite Element Exterior Calculus","author":"DN Arnold","year":"2018","unstructured":"Arnold, D.N.: Finite Element Exterior Calculus. SIAM (2018)"},{"key":"9498_CR7","doi-asserted-by":"crossref","unstructured":"Arnold, D.N., Falk, R.S., Winther, R.: Differential complexes and stability of finite element methods II: The elasticity complex. In: D.\u00a0Arnold, P.\u00a0Bochev, R.\u00a0Lehoucq, R.\u00a0Nicolaides, M.\u00a0Shashkov (eds.) Compatible Spatial Discretizations, IMA Vol. Math. Appl., vol. 142, pp. 47\u201368. Springer, Berlin (2006)","DOI":"10.1007\/0-387-38034-5_3"},{"key":"9498_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492906210018","volume":"15","author":"DN Arnold","year":"2006","unstructured":"Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus, homological techniques, and applications. Acta Numerica 15, 1 (2006)","journal-title":"Acta Numerica"},{"issue":"260","key":"9498_CR9","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1090\/S0025-5718-07-01998-9","volume":"76","author":"DN Arnold","year":"2007","unstructured":"Arnold, D.N., Falk, R.S., Winther, R.: Mixed finite element methods for linear elasticity with weakly imposed symmetry. Mathematics of Computation 76(260), 1699\u20131723 (2007)","journal-title":"Mathematics of Computation"},{"issue":"2","key":"9498_CR10","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1090\/S0273-0979-10-01278-4","volume":"47","author":"DN Arnold","year":"2010","unstructured":"Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus: from Hodge theory to numerical stability. Bulletin of the American Mathematical Society 47(2), 281\u2013354 (2010)","journal-title":"Bulletin of the American Mathematical Society"},{"issue":"3","key":"9498_CR11","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s002110100348","volume":"92","author":"DN Arnold","year":"2002","unstructured":"Arnold, D.N., Winther, R.: Mixed finite elements for elasticity. Numerische Mathematik 92(3), 401\u2013419 (2002)","journal-title":"Numerische Mathematik"},{"key":"9498_CR12","doi-asserted-by":"crossref","unstructured":"Beig, R.: TT-tensors and conformally flat structures on 3-manifolds. In: Mathematics of Gravitation, Part I, pp. 109\u2013118. Polish Academy of Sciences, Warsaw (1997)","DOI":"10.4064\/-41-1-109-118"},{"key":"9498_CR13","doi-asserted-by":"crossref","unstructured":"Beig, R., Chrusciel, P.T.: On linearised vacuum constraint equations on Einstein manifolds. Classical and Quantum Gravity 37(21), 215012 (2020)","DOI":"10.1088\/1361-6382\/ab81cc"},{"key":"9498_CR14","unstructured":"Bossavit, A.: Computational Electromagnetism. Academic Press (Boston) (1998)"},{"issue":"4","key":"9498_CR15","doi-asserted-by":"publisher","first-page":"2496","DOI":"10.1137\/16M1073662","volume":"49","author":"D Breit","year":"2017","unstructured":"Breit, D., Cianchi, A., Diening, L.: Trace-free Korn inequalities in Orlicz spaces. SIAM Journal on Mathematical Analysis 49(4), 2496\u20132526 (2017)","journal-title":"SIAM Journal on Mathematical Analysis"},{"issue":"1","key":"9498_CR16","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1016\/0022-1236(92)90147-B","volume":"108","author":"J Br\u00fcning","year":"1992","unstructured":"Br\u00fcning, J., Lesch, M.: Hilbert complexes. Journal of Functional Analysis 108(1), 88\u2013132 (1992)","journal-title":"Journal of Functional Analysis"},{"issue":"1","key":"9498_CR17","doi-asserted-by":"publisher","first-page":"97","DOI":"10.2307\/3062111","volume":"154","author":"A \u010cap","year":"2001","unstructured":"\u010cap, A., Slov\u00e1k, J., Sou\u010dek, V.: Bernstein-Gelfand-Gelfand sequences. Annals of Mathematics 154(1), 97\u2013113 (2001)","journal-title":"Annals of Mathematics"},{"issue":"23","key":"9498_CR18","doi-asserted-by":"publisher","first-page":"235001","DOI":"10.1103\/PhysRevLett.99.235001","volume":"99","author":"L Chac\u00f3n","year":"2007","unstructured":"Chac\u00f3n, L., Simakov, A.N., Zocco, A.: Steady-state properties of driven magnetic reconnection in 2d electron magnetohydrodynamics. Physical review letters 99(23), 235001 (2007)","journal-title":"Physical review letters"},{"issue":"2","key":"9498_CR19","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s00211-017-0939-x","volume":"139","author":"SH Christiansen","year":"2018","unstructured":"Christiansen, S.H., Hu, J., Hu, K.: Nodal finite element de Rham complexes. Numerische Mathematik 139(2), 411\u2013446 (2018)","journal-title":"Numerische Mathematik"},{"key":"9498_CR20","doi-asserted-by":"crossref","unstructured":"Christiansen, S.H., Hu, K., Sande, E.: Poincar\u00e9 path integrals for elasticity. Journal de Math\u00e9matiques Pures et Appliqu\u00e9es (2019)","DOI":"10.1016\/j.matpur.2019.06.002"},{"key":"9498_CR21","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.G.: Linear and nonlinear functional analysis with applications, vol. 130. SIAM (2013)","DOI":"10.1137\/1.9781611972597"},{"key":"9498_CR22","unstructured":"Ciarlet, P.G., Gratie, L., Mardare, C.: Intrinsic methods in elasticity: A mathematical survey. Discrete and Continuous Dynamical Systems (2009)"},{"issue":"2","key":"9498_CR23","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00209-009-0517-8","volume":"265","author":"M Costabel","year":"2010","unstructured":"Costabel, M., McIntosh, A.: On Bogovski\u012d and regularized Poincar\u00e9 integral operators for de Rham complexes on Lipschitz domains. Mathematische Zeitschrift 265(2), 297\u2013320 (2010)","journal-title":"Mathematische Zeitschrift"},{"issue":"4","key":"9498_CR24","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s00526-005-0371-4","volume":"25","author":"S Dain","year":"2006","unstructured":"Dain, S.: Generalized Korn\u2019s inequality and conformal Killing vectors. Calculus of variations and partial differential equations 25(4), 535\u2013540 (2006)","journal-title":"Calculus of variations and partial differential equations"},{"key":"9498_CR25","first-page":"1368","volume":"46","author":"M Eastwood","year":"1999","unstructured":"Eastwood, M.: Variations on the de Rham complex. Notices AMS 46, 1368\u20131376 (1999)","journal-title":"Notices AMS"},{"key":"9498_CR26","unstructured":"Eastwood, M.: A complex from linear elasticity. In: Proceedings of the 19th Winter School\u201d Geometry and Physics\u201d, pp. 23\u201329. Circolo Matematico di Palermo (2000)"},{"key":"9498_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8843-0","volume-title":"Singular limits in thermodynamics of viscous fluids","author":"E Feireisl","year":"2009","unstructured":"Feireisl, E., Novotn\u1ef3, A.: Singular limits in thermodynamics of viscous fluids. Springer (2009)"},{"issue":"6","key":"9498_CR28","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1007\/s00013-009-0067-7","volume":"93","author":"M Fuchs","year":"2009","unstructured":"Fuchs, M., Schirra, O.: An application of a new coercive inequality to variational problems studied in general relativity and in Cosserat elasticity giving the smoothness of minimizers. Archiv der Mathematik 93(6), 587 (2009)","journal-title":"Archiv der Mathematik"},{"key":"9498_CR29","first-page":"175","volume":"123","author":"G Geymonat","year":"2005","unstructured":"Geymonat, G., Krasucki, F.: Some remarks on the compatibility conditions in elasticity. Accad. Naz. Sci. XL 123, 175\u2013182 (2005)","journal-title":"Accad. Naz. Sci. XL"},{"issue":"5","key":"9498_CR30","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/j.crma.2005.12.031","volume":"342","author":"G Geymonat","year":"2006","unstructured":"Geymonat, G., Krasucki, F.: Beltrami\u2019s solutions of general equilibrium equations in continuum mechanics. Comptes Rendus Mathematique 342(5), 359\u2013363 (2006)","journal-title":"Comptes Rendus Mathematique"},{"issue":"5","key":"9498_CR31","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1023\/A:1025924417135","volume":"44","author":"NV Glotko","year":"2003","unstructured":"Glotko, N.V.: On the complex of Sobolev spaces associated with an abstract Hilbert complex. Siberian Mathematical Journal 44(5), 774\u2013792 (2003)","journal-title":"Siberian Mathematical Journal"},{"key":"9498_CR32","doi-asserted-by":"crossref","unstructured":"Gopalakrishnan, J., Lederer, P.L., Sch\u00f6berl, J.: A mass conserving mixed stress formulation for the Stokes equations. IMA Journal on Numerical Analysis 40(3), 1838\u20131874 (2020)","DOI":"10.1093\/imanum\/drz022"},{"key":"9498_CR33","doi-asserted-by":"crossref","unstructured":"Gopalakrishnan, J., Lederer, P.L., Sch\u00f6berl, J.: A mass conserving mixed stress formulation for Stokes flow with weakly imposed stress symmetry. SIAM Journal on Numerical Analysis 58(1), 706\u2013732 (2020)","DOI":"10.1137\/19M1248960"},{"issue":"July 03","key":"9498_CR34","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1017\/S0962492902000041","volume":"11","author":"R Hiptmair","year":"2002","unstructured":"Hiptmair, R.: Finite elements in computational electromagnetism. Acta Numerica 11(July 2003), 237\u2013339 (2002)","journal-title":"Acta Numerica"},{"issue":"2","key":"9498_CR35","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.jfa.2012.04.016","volume":"263","author":"R Hiptmair","year":"2012","unstructured":"Hiptmair, R., Li, J., Zou, J.: Universal extension for Sobolev spaces of differential forms and applications. J. Funct. Anal 263(2), 364\u2013382 (2012)","journal-title":"J. Funct. Anal"},{"key":"9498_CR36","doi-asserted-by":"crossref","unstructured":"Hiptmair, R., Pechstein, C.: Discrete regular decompositions of tetrahedral discrete 1-forms. In: U.\u00a0Langer, D.\u00a0Pauly, S.I. Repin (eds.) Maxwell\u2019s Equations: Analysis and Numerics, chap.\u00a07. Walter de Gruyter GmbH & Co KG (2019)","DOI":"10.1515\/9783110543612-007"},{"issue":"4","key":"9498_CR37","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1137\/1037123","volume":"37","author":"CO Horgan","year":"1995","unstructured":"Horgan, C.O.: Korn\u2019s inequalities and their applications in continuum mechanics. SIAM review 37(4), 491\u2013511 (1995)","journal-title":"SIAM review"},{"key":"9498_CR38","unstructured":"H\u00f6rmander, L.: The analysis of linear partial differential operators III: Pseudo-differential operators, vol. 274. Springer Science & Business Media (1994)"},{"issue":"7","key":"9498_CR39","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1002\/zamm.200800218","volume":"89","author":"J Jeong","year":"2009","unstructured":"Jeong, J., Ram\u00e9zani, H., M\u00fcnch, I., Neff, P.: A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature. ZAMM-Journal of Applied Mathematics and Mechanics\/Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics 89(7), 552\u2013569 (2009)","journal-title":"ZAMM-Journal of Applied Mathematics and Mechanics\/Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics"},{"issue":"1","key":"9498_CR40","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1146\/annurev.ms.05.080175.000355","volume":"5","author":"E Kr\u00f6ner","year":"1975","unstructured":"Kr\u00f6ner, E., Anthony, K.: Dislocations and disclinations in material structures: The basic topological concepts. Annual review of materials science 5(1), 43\u201372 (1975)","journal-title":"Annual review of materials science"},{"issue":"1","key":"9498_CR41","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/BF00253946","volume":"11","author":"R Mindlin","year":"1962","unstructured":"Mindlin, R., Tiersten, H.: Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and analysis 11(1), 415\u2013448 (1962)","journal-title":"Archive for Rational Mechanics and analysis"},{"issue":"2","key":"9498_CR42","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1002\/zamm.200800156","volume":"89","author":"P Neff","year":"2009","unstructured":"Neff, P., Jeong, J.: A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy. ZAMM-Journal of Applied Mathematics and Mechanics\/Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik 89(2), 107\u2013122 (2009)","journal-title":"ZAMM-Journal of Applied Mathematics and Mechanics\/Zeitschrift f\u00fcr Angewandte Mathematik und Mechanik"},{"issue":"5","key":"9498_CR43","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1007\/s00033-006-6073-8","volume":"59","author":"S Park","year":"2008","unstructured":"Park, S., Gao, X.L.: Variational formulation of a modified couple stress theory and its application to a simple shear problem. Zeitschrift f\u00fcr angewandte Mathematik und Physik 59(5), 904\u2013917 (2008)","journal-title":"Zeitschrift f\u00fcr angewandte Mathematik und Physik"},{"issue":"2","key":"9498_CR44","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1515\/anly-2018-0027","volume":"39","author":"D Pauly","year":"2019","unstructured":"Pauly, D.: A global div-curl-lemma for mixed boundary conditions in weak Lipschitz domains and a corresponding generalized $$A_{0}^{\\ast }$$-$$A_{1}$$-lemma in Hilbert spaces. Analysis 39(2), 33\u201358 (2019)","journal-title":"Analysis"},{"key":"9498_CR45","unstructured":"Pauly, D., Zulehner, W.: On closed and exact Grad-grad-and div-Div-complexes, corresponding compact embeddings for tensor rotations, and a related decomposition result for biharmonic problems in 3D. arXiv preprint arXiv:1609.05873v4 (2016)"},{"key":"9498_CR46","doi-asserted-by":"crossref","unstructured":"Pauly, D., Zulehner, W.: The divDiv-complex and applications to biharmonic equations. Applicable Analysis pp. 1\u201352 (2018)","DOI":"10.1080\/00036811.2018.1542685"},{"issue":"2","key":"9498_CR47","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/BF01161700","volume":"187","author":"R Picard","year":"1984","unstructured":"Picard, R.: An elementary proof for a compact imbedding result in generalized electromagnetic theory. Mathematische Zeitschrift 187(2), 151\u2013164 (1984)","journal-title":"Mathematische Zeitschrift"},{"key":"9498_CR48","unstructured":"Quenneville-B\u00e9lair, V.: A New Approach to Finite Element Simulations of General Relativity. Ph.D. thesis, University of Minnesota (2015)"},{"issue":"7","key":"9498_CR49","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1002\/pssb.19610010702","volume":"1","author":"A Seeger","year":"1961","unstructured":"Seeger, A.: Recent advances in the theory of defects in crystals. Physica Status Solidi (B) 1(7), 669\u2013698 (1961)","journal-title":"Physica Status Solidi (B)"},{"key":"9498_CR50","doi-asserted-by":"crossref","unstructured":"Van\u00a0Goethem, N.: The non-Riemannian dislocated crystal: A tribute to Ekkehart Kr\u00f6ner (1919-2000). Journal of Geometric Mechanics 2, 303\u2013320 (2010)","DOI":"10.3934\/jgm.2010.2.303"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09498-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10208-021-09498-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09498-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T14:43:42Z","timestamp":1697985822000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10208-021-09498-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,5]]},"references-count":50,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["9498"],"URL":"https:\/\/doi.org\/10.1007\/s10208-021-09498-9","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,5]]},"assertion":[{"value":"26 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}