{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T02:20:10Z","timestamp":1648952410954},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,8,9]],"date-time":"2005-08-09T00:00:00Z","timestamp":1123545600000},"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":[[2005,10]]},"DOI":"10.1007\/s00211-005-0623-4","type":"journal-article","created":{"date-parts":[[2005,8,9]],"date-time":"2005-08-09T13:39:53Z","timestamp":1123594793000},"page":"573-599","source":"Crossref","is-referenced-by-count":1,"title":["Error estimates in W2,\u221e-semi-norms for discrete interpolating D2-splines"],"prefix":"10.1007","volume":"101","author":[{"given":"R\u00e9mi","family":"Arcang\u00e9li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mar\u00eda Cruz L\u00f3pez de","family":"Silanes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Jos\u00e9","family":"Torrens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,8,9]]},"reference":[{"key":"623_CR1","doi-asserted-by":"crossref","unstructured":"Arcang\u00e9li, R., L\u00f3pez de Silanes, M. C., Torrens J. J.: Multidimensional Minimizing Splines. Kluwer Academic Publishers, Boston, 2004","DOI":"10.1007\/b130045"},{"key":"623_CR2","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1137\/0726068","volume":"26","author":"Bernardi","year":"5","unstructured":"Bernardi, C.: Optimal-finite element interpolation on curved domains. SIAM J. Numer. Anal. 26(5), 1212-1240 (1989)","journal-title":"SIAM J. Numer. Anal."},{"key":"623_CR3","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1137\/S0036142995293766","volume":"35","author":"Bernardi","year":"5","unstructured":"Bernardi, C., Girault, V.: A local regularization operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35(5), 1893\u20131916 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"623_CR4","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York, 2002","DOI":"10.1007\/978-1-4757-3658-8"},{"key":"623_CR5","doi-asserted-by":"crossref","first-page":"3301","DOI":"10.1090\/S0002-9947-1995-1311906-6","volume":"347","author":"Chui","year":"9","unstructured":"Chui, C.K., Hong, D., Jia, R.Q.: Stability of optimal-order approximation by bivariate splines over arbitrary triangulations. Trans. Amer. Math. Soc. 347(9), 3301\u20133318 (1995)","journal-title":"Trans. Amer. Math. Soc."},{"key":"623_CR6","unstructured":"Ciarlet, P.G.: Introduction \u00e0 l'Analyse Num\u00e9rique Matricielle et \u00e0 l'Optimisation. In: Collection Math\u00e9matiques Appliqu\u00e9es pour la Ma\u00eetrise. Masson, Paris, 1990 Fourth English edition by Cambridge University Press, 1989"},{"key":"623_CR7","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems, volume 40 of Classics in Applied Mathematics. SIAM Philadelphia, 2002. Firstly published by North-Holland, Amsterdam, 1978","DOI":"10.1137\/1.9780898719208"},{"key":"623_CR8","doi-asserted-by":"crossref","unstructured":"Cl\u00e9ment, P.: Approximation by finite element methods using local regularization. Rairo, R-2, 77\u201384 (1975)","DOI":"10.1051\/m2an\/197509R200771"},{"key":"623_CR9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s003650010034","volume":"17","author":"Davydov","year":"2001","unstructured":"Davydov, O., N\u00fcrnberger, G., Zeilfelder F.: Bivariate spline interpolation with optimal approximation order. Constr. Approx. 17, 181\u2013208 (2001)","journal-title":"Constr. Approx."},{"key":"623_CR10","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1006\/jath.2001.3577","volume":"111","author":"Davydov","year":"2001","unstructured":"Davydov, O.: Stable local bases for multivariate spline spaces. J. Approx. Theory 111, 267\u2013297 (2001)","journal-title":"J. Approx. Theory"},{"key":"623_CR11","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s00365-001-0006-8","volume":"18","author":"Davydov","year":"2002","unstructured":"Davydov, O., Schumaker, L.L.: On stable local bases for bivariate polynomial spline spaces. Constr. Approx. 18, 87\u2013116 (2002)","journal-title":"Constr. Approx."},{"key":"623_CR12","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01400302","volume":"23","author":"Douglas","year":"1975","unstructured":"Douglas, Jr.J., Dupont, T., Wahlbin, L.: The stability in Lq of the L2-projection into finite element function spaces. Numer. Math. 23, 193\u2013197 (1975)","journal-title":"Numer. Math."},{"key":"623_CR13","doi-asserted-by":"crossref","unstructured":"Douglas, Jr.J., Dupont, T., Wahlbin, L.: Optimal L\u221e error estimates for Galerkin approximations to solutions of two-point boundary value problems. Math. Comp. 29 475\u2013483 (1975)","DOI":"10.2307\/2005565"},{"key":"623_CR14","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1090\/S0025-5718-1980-0559195-7","volume":"34","author":"Dupont","year":"1980","unstructured":"Dupont, T., Scott, L.R.: Polynomial approximation of functions in Sobolev spaces. Math. Comp. 34, 441\u2013463 (1980)","journal-title":"Math. Comp."},{"key":"623_CR15","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1090\/S0025-5718-02-01446-1","volume":"71","author":"Girault","year":"239","unstructured":"Girault, V., Scott, L.R.: Hermite interpolation of nonsmooth functions preserving boundary conditions. Math. Comp. 71 (239), 1043\u20131074 (2002)","journal-title":"Math. Comp."},{"key":"623_CR16","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s00365-001-0018-4","volume":"18","author":"Golitschek","year":"2002","unstructured":"von Golitschek, M., Schumaker, L.L.: Bounds on projections onto bivariate polynomial spline spaces with stable local bases. Constr. Approx. 18, 241\u2013254 (2002)","journal-title":"Constr. Approx."},{"key":"623_CR17","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s002110100381","volume":"93","author":"Golitschek","year":"2002","unstructured":"von Golitschek, M., Lai, M.-J., Schumaker, L.L.: Error bounds for minimal energy bivariate polynomial splines. Numer. Math. 93, 315\u2013331 (2002)","journal-title":"Numer. Math."},{"key":"623_CR18","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1023\/A:1018958011262","volume":"9","author":"Lai","year":"1998","unstructured":"Lai, M.-J., Schumaker, L.L.: On the approximation power of bivariate splines. Adv. in Comput. Math. 9, 251\u2013279 (1998)","journal-title":"Adv. in Comput. Math."},{"key":"623_CR19","unstructured":"Le M\u00e9haut\u00e9 A.: Interpolation et Approximation par des Fonctions Polynomiales par Morceaux dans \u211dn. Universit\u00e9 de Rennes, Th\u00e8se d'\u00c9tat, 1984"},{"key":"623_CR20","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/BF01404469","volume":"53","author":"Silanes","year":"1988","unstructured":"L\u00f3pez de Silanes, M.C., Apprato, D.: Estimations de l'erreur d'approximation sur un domaine born\u00e9 de \u211dn par Dm-splines d'interpolation et d'ajustement discr\u00e8tes. Numer. Math. 53, 367\u2013376 (1988)","journal-title":"Numer. Math."},{"key":"623_CR21","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1002\/nme.1620150214","volume":"15","author":"Nielson","year":"1978","unstructured":"Nielson, G.M.: A first-order blending method for triangles based upon cubic interpolation. Int. J. Numer. Meth. Engrg. 15, 308\u2013318 (1978)","journal-title":"Int. J. Numer. Meth. Engrg."},{"key":"623_CR22","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1137\/0726055","volume":"26","author":"Schumaker","year":"4","unstructured":"Schumaker, L.L.: On super splines and finite elements. SIAM J. Numer. Anal. 26(4), 997\u20131005 (1989)","journal-title":"SIAM J. Numer. Anal."},{"key":"623_CR23","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"Scott","year":"190","unstructured":"Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54(190), 483\u2013493 (1990)","journal-title":"Math. Comp."},{"key":"623_CR24","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01395933","volume":"19","author":"Strang","year":"1972","unstructured":"Strang, G.: Approximation in the Finite Element Method. Numer. Math. 19, 81\u201398 (1972)","journal-title":"Numer. Math."},{"key":"623_CR25","doi-asserted-by":"crossref","unstructured":"\u017den\u00ed\u0161ek, A.: A general theorem on triangular finite C(m)-elements. Rairo, R-2, 119\u2013127 (1974)","DOI":"10.1051\/m2an\/197408R201191"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0623-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-005-0623-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0623-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T20:01:06Z","timestamp":1586376066000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-005-0623-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,9]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["623"],"URL":"https:\/\/doi.org\/10.1007\/s00211-005-0623-4","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,9]]}}}