{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T05:40:38Z","timestamp":1747460438143,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2016,8,10]],"date-time":"2016-08-10T00:00:00Z","timestamp":1470787200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/04106\/2013"],"award-info":[{"award-number":["UID\/MAT\/04106\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 1462"],"award-info":[{"award-number":["GRK 1462"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Anal. Oper. Theory"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s11785-016-0583-y","type":"journal-article","created":{"date-parts":[[2016,8,10]],"date-time":"2016-08-10T04:51:15Z","timestamp":1470804675000},"page":"1221-1240","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Error Estimates for the Coupling of Analytical and Numerical Solutions"],"prefix":"10.1007","volume":"11","author":[{"given":"Klaus","family":"G\u00fcrlebeck","sequence":"first","affiliation":[]},{"given":"Uwe","family":"K\u00e4hler","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0028-5793","authenticated-orcid":false,"given":"Dmitrii","family":"Legatiuk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,10]]},"reference":[{"key":"583_CR1","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1063\/1.4756124","volume":"1479","author":"S Bock","year":"2012","unstructured":"Bock, S., G\u00fcrlebeck, K., Legatiuk, D.: On a special finite element based on holomorphic functions. AIP Conf. Proc. 1479, 308 (2012)","journal-title":"AIP Conf. Proc."},{"key":"583_CR2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1002\/mma.1033","volume":"32","author":"S Bock","year":"2009","unstructured":"Bock, S., G\u00fcerlebeck, K.: On a spatial generalization of the Kolosov\u2013Muskhelishvili formulae. Math. Methods Appl. Sci. 32, 223\u2013240 (2009)","journal-title":"Math. Methods Appl. Sci."},{"key":"583_CR3","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1007\/s00006-014-0490-0","volume":"24","author":"S Bock","year":"2014","unstructured":"Bock, S.: On monogenic series expansions with applications to linear elasticity. Adv. Appl. Clifford Algebras 24, 931\u2013943 (2014)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"583_CR4","doi-asserted-by":"crossref","first-page":"5114","DOI":"10.1002\/mma.3431","volume":"38","author":"S Bock","year":"2015","unstructured":"Bock, S., G\u00fcrlebeck, K., Legatiuk, D., Nguyen, H.M.: \n                        $$\\psi $$\n                        \n                            \n                                            \n                                \u03c8\n                            \n                        \n                    -Hyperholomorphic functions and a Kolosov-Muskhelishvili formula. Math. Methods Appl. Sci. 38, 5114\u20135123 (2015)","journal-title":"Math. Methods Appl. Sci."},{"key":"583_CR5","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, Amsterdam (1978)"},{"key":"583_CR6","volume-title":"Interpolation and Approximation","author":"PJ Davis","year":"1975","unstructured":"Davis, P.J.: Interpolation and Approximation. Dover, New York (1975)"},{"issue":"2","key":"583_CR7","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9939-96-03132-2","volume":"123","author":"Z Ding","year":"1996","unstructured":"Ding, Z.: A proof of the trace theorem of Sobolev spaces on Lipschitz domains. Proc. Am. Math. Soc. 123(2), 591\u2013600 (1996)","journal-title":"Proc. Am. Math. Soc."},{"unstructured":"Ferreira, P.J.S.G.: Superresolution, the recovery of missing samples and Vandermonde matrices on the unit circle. In: Proceedings of the 1999 Workshop on Sampling Theory and Applications, Loen (1999)","key":"583_CR8"},{"key":"583_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4814-9","volume-title":"Lecture on Complex Approximation","author":"D Gaier","year":"1987","unstructured":"Gaier, D.: Lecture on Complex Approximation. Birkh\u00e4user, Boston (1987)"},{"unstructured":"G\u00fcrlebeck, K., Legatiuk, D.: On the continuous coupling of finite elements with holomorphic basis functions. Hypercomplex Analysis: New Perspectives and Applications. Birkh\u00e4user, Basel. ISBN 978-3-319-08770-2","key":"583_CR10"},{"doi-asserted-by":"publisher","unstructured":"G\u00fcrlebeck, K., K\u00e4hler, U., Legatiuk, D.: Interpolation problem arising in a coupling of finite element method with holomorphic basis functions. AIP Conf. Proc. 1648 (2015). doi:\n                        10.1063\/1.4912655","key":"583_CR11","DOI":"10.1063\/1.4912655"},{"doi-asserted-by":"publisher","unstructured":"Legatiuk, D., Nguyen, H.M.: Improved convergence results for the finite element method with holomorphic functions. Adv. Appl. Clifford Algebra (2014). doi:\n                        10.1007\/s00006-014-0501-1","key":"583_CR12","DOI":"10.1007\/s00006-014-0501-1"},{"unstructured":"Legatiuk, D.: Evaluation of the coupling between an analytical and a numerical solution for boundary value problems with singularities. Ph.D. thesis (2015). ISBN: 978-3-95773-193-7","key":"583_CR13"},{"key":"583_CR14","volume-title":"Fracture, an advanced treatise. Mathematical Fundamentals","author":"H Liebowitz","year":"1968","unstructured":"Liebowitz, H.: Fracture, an advanced treatise. Mathematical Fundamentals, vol. II. Academic Press, London (1968)"},{"doi-asserted-by":"crossref","unstructured":"Lurie, A.I.: Theory of Elasticity. Foundations of Engineering Mechanics. Springer, Berlin (2005) (translated from Russian)","key":"583_CR15","DOI":"10.1007\/978-3-540-26455-2"},{"unstructured":"Mu\u00dfchelischwili, N.I.: Einige Grundaufgaben der mathematischen Elastizit\u00e4tstheorie. VEB Fachbuchverlag Leipzig (1971)","key":"583_CR16"},{"key":"583_CR17","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1002\/nme.1620210809","volume":"21","author":"R Piltner","year":"1985","unstructured":"Piltner, R.: Special finite elements with holes and internal cracks. Int. J. Numer. Methods Eng. 21, 509\u2013528 (1985)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"583_CR18","first-page":"597","volume":"10","author":"R Piltner","year":"2003","unstructured":"Piltner, R.: The derivation of special purpose element functions using complex solution representation. Comput. Assist. Mech. Eng. Sci. 10(4), 597\u2013607 (2003)","journal-title":"Comput. Assist. Mech. Eng. Sci."},{"issue":"12\u201313","key":"583_CR19","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.finel.2008.04.005","volume":"44","author":"R Piltner","year":"2008","unstructured":"Piltner, R.: Some remarks on finite elements with an elliptic hole. Finite Elements Anal. Design 44(12\u201313), 767\u2013772 (2008)","journal-title":"Finite Elements Anal. Design"},{"key":"583_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618994","volume-title":"Spline Functions on Triangulation","author":"L Schumaker","year":"2007","unstructured":"Schumaker, L.: Spline Functions on Triangulation. Cambridge University Press, Cambridge (2007)"}],"container-title":["Complex Analysis and Operator Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11785-016-0583-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11785-016-0583-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11785-016-0583-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11785-016-0583-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T02:33:16Z","timestamp":1495765996000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11785-016-0583-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,10]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["583"],"URL":"https:\/\/doi.org\/10.1007\/s11785-016-0583-y","relation":{},"ISSN":["1661-8254","1661-8262"],"issn-type":[{"type":"print","value":"1661-8254"},{"type":"electronic","value":"1661-8262"}],"subject":[],"published":{"date-parts":[[2016,8,10]]}}}