{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T05:36:09Z","timestamp":1674279369858},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,9,10]],"date-time":"2014-09-10T00:00:00Z","timestamp":1410307200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s10915-014-9912-3","type":"journal-article","created":{"date-parts":[[2014,9,9]],"date-time":"2014-09-09T11:09:46Z","timestamp":1410260986000},"page":"769-798","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Contraction and Optimality Properties of an Adaptive Legendre\u2013Galerkin Method: The Multi-Dimensional Case"],"prefix":"10.1007","volume":"63","author":[{"given":"Claudio","family":"Canuto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valeria","family":"Simoncini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Verani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,9,10]]},"reference":[{"key":"9912_CR1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1098\/rspl.1878.0016","volume":"27","author":"J Adams","year":"1878","unstructured":"Adams, J.: On the expression of the product of any two legendres coefficients by means of a series of legendres coefficients. Proc. R. Soc. Lond. 27, 63\u201371 (1878)","journal-title":"Proc. R. Soc. Lond."},{"key":"9912_CR2","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/0022-1236(72)90011-0","volume":"9","author":"MS Baouendi","year":"1972","unstructured":"Baouendi, M.S., Goulaouic, C.: R\u00e9gularit\u00e9 analytique et it\u00e9r\u00e9s d\u2019op\u00e9rateurs elliptiques d\u00e9g\u00e9n\u00e9r\u00e9s; applications. J. Funct. Anal. 9, 208\u2013248 (1972)","journal-title":"J. Funct. Anal."},{"key":"9912_CR3","doi-asserted-by":"crossref","unstructured":"Benzi, M., T\u016fma, M.: Orderings for factorized sparse approximate inverse preconditioners. SIAM J. Sci. Comput. 21(5), 1851\u20131868 (electronic), 2000. Iterative methods for solving systems of algebraic equations (Copper Mountain, CO, 1998)","DOI":"10.1137\/S1064827598339372"},{"key":"9912_CR4","unstructured":"Binev, P.: Tree approximation for $$hp$$ h p -adaptivity. (in preparation)"},{"key":"9912_CR5","unstructured":"Binev, P.: Instance optimality for $$hp$$ h p -type approximation. Technical Report 39, Mathematisches Forschungsinstitut Oberwolfach (2013)"},{"issue":"2","key":"9912_CR6","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s00211-003-0492-7","volume":"97","author":"P Binev","year":"2004","unstructured":"Binev, P., Dahmen, W., DeVore, R.: Adaptive finite element methods with convergence rates. Numer. Math. 97(2), 219\u2013268 (2004)","journal-title":"Numer. Math."},{"issue":"11","key":"9912_CR7","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1016\/j.apnum.2011.07.008","volume":"61","author":"M B\u00fcrg","year":"2011","unstructured":"B\u00fcrg, M., D\u00f6rfler, W.: Convergence of an adaptive $$hp$$ h p finite element strategy in higher space-dimensions. Appl. Numer. Math. 61(11), 1132\u20131146 (2011)","journal-title":"Appl. Numer. Math."},{"key":"9912_CR8","unstructured":"Canuto, C., Nochetto, R., Stevenson, R., Verani, M.: An $$hp$$ h p adaptive finite element method: convergence and optimality properties. (in preparation)"},{"issue":"4","key":"9912_CR9","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1016\/j.camwa.2013.05.025","volume":"67","author":"C Canuto","year":"2014","unstructured":"Canuto, C., Nochetto, R., Verani, M.: Contraction and optimality properties of adaptive Legendre\u2013Galerkin methods: the 1-dimensional case. Comput. Math. Appl. 67(4), 752\u2013770 (2014)","journal-title":"Comput. Math. Appl."},{"key":"9912_CR10","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1090\/S0025-5718-2013-02781-0","volume":"83","author":"C Canuto","year":"2014","unstructured":"Canuto, C., Nochetto, R.H., Verani, M.: Adaptive Fourier\u2013Galerkin methods. Math. Comput. 83, 1645\u20131687 (2014)","journal-title":"Math. Comput."},{"key":"9912_CR11","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.laa.2014.03.029","volume":"452","author":"C Canuto","year":"2014","unstructured":"Canuto, C., Simoncini, V., Verani, M.: On the decay of the inverse of matrices that are sum of Kronecker products. Linear Algebra Appl. 452, 21\u201339 (2014)","journal-title":"Linear Algebra Appl."},{"key":"9912_CR12","doi-asserted-by":"crossref","unstructured":"Canuto, C., Verani, M.: On the numerical analysis of adaptive spectral\/hp methods for elliptic problems. In: Brezzi, F. et al. (eds.) Analysis and Numerics of Partial Differential Equations, pp. 165\u2013192. Springer INdAM series (2013)","DOI":"10.1007\/978-88-470-2592-9_11"},{"issue":"5","key":"9912_CR13","doi-asserted-by":"crossref","first-page":"2524","DOI":"10.1137\/07069047X","volume":"46","author":"JM Cascon","year":"2008","unstructured":"Cascon, J.M., Kreuzer, C., Nochetto, R.H., Siebert, K.G.: Quasi-optimal convergence rate for an adaptive finite element method. SIAM J. Numer. Anal. 46(5), 2524\u20132550 (2008)","journal-title":"SIAM J. Numer. Anal."},{"key":"9912_CR14","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1090\/S0025-5718-00-01252-7","volume":"70","author":"A Cohen","year":"1998","unstructured":"Cohen, A., Dahmen, W., DeVore, R.: Adaptive wavelet methods for elliptic operator equations: convergence rates. Math. Comput. 70, 27\u201375 (1998)","journal-title":"Math. Comput."},{"issue":"5","key":"9912_CR15","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s10208-012-9120-1","volume":"12","author":"A Cohen","year":"2012","unstructured":"Cohen, A., DeVore, R., Nochetto, R.H.: Convergence rates of AFEM with $$H^{-1}$$ H - 1 data. Found. Comput. Math. 12(5), 671\u2013718 (2012)","journal-title":"Found. Comput. Math."},{"issue":"3","key":"9912_CR16","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1137\/0733054","volume":"33","author":"W D\u00f6rfler","year":"1996","unstructured":"D\u00f6rfler, W.: A convergent adaptive algorithm for Poisson\u2019s equation. SIAM J. Numer. Anal. 33(3), 1106\u20131124 (1996)","journal-title":"SIAM J. Numer. Anal."},{"issue":"10","key":"9912_CR17","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1016\/j.apnum.2006.10.003","volume":"57","author":"W D\u00f6rfler","year":"2007","unstructured":"D\u00f6rfler, W., Heuveline, V.: Convergence of an adaptive $$hp$$ h p finite element strategy in one space dimension. Appl. Numer. Math. 57(10), 1108\u20131124 (2007)","journal-title":"Appl. Numer. Math."},{"key":"9912_CR18","volume-title":"Direct Methods for Sparse Matrices","author":"IS Duff","year":"1989","unstructured":"Duff, I.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse Matrices. Clarendon Press, Oxford (1989)"},{"key":"9912_CR19","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD (1996)"},{"issue":"6","key":"9912_CR20","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1007\/BF01389735","volume":"49","author":"W Gui","year":"1986","unstructured":"Gui, W., Babu\u0161ka, I.: The $$h,\\;p$$ h , p and $$h$$ h - $$p$$ p versions of the finite element method in 1 dimension. III. The adaptive $$h$$ h - $$p$$ p version. Numer. Math. 49(6), 659\u2013683 (1986)","journal-title":"Numer. Math."},{"issue":"3","key":"9912_CR21","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1214\/09-AOS764","volume":"38","author":"P Hall","year":"2010","unstructured":"Hall, P., Jin, J.: Innovated higher criticism for detecting sparse signals in correlated noise. Ann. Stat. 38(3), 1686\u20131732 (2010)","journal-title":"Ann. Stat."},{"key":"9912_CR22","unstructured":"Jaffard, S.: Propri\u00e9t\u00e9s des matrices \u201cbien localis\u00e9es\u201d pr\u00e8s de leur diagonale et quelques applications. Annales de l\u2019I.H.P. 5, 461\u2013476 (1990)"},{"key":"9912_CR23","unstructured":"Krishtal, I., Strohmer, T., Wertz, T.: Localization of matrix factorizations (2013). arXiv:1305.1618"},{"issue":"1","key":"9912_CR24","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s002110050208","volume":"74","author":"J-F Maitre","year":"1996","unstructured":"Maitre, J.-F., Pourquier, O.: Condition number and diagonal preconditioning: comparison of the $$p$$ p -version and the spectral element methods. Numer. Math. 74(1), 69\u201384 (1996)","journal-title":"Numer. Math."},{"key":"9912_CR25","doi-asserted-by":"crossref","unstructured":"Mitchell, W.F., McClain, M.A.: A survey of $$hp$$ h p -adaptive strategies for elliptic partial differential equations. In: Recent Advances in Computational and Applied Mathematics, pp. 227\u2013258. Springer, Dordrecht (2011)","DOI":"10.1007\/978-90-481-9981-5_10"},{"issue":"2","key":"9912_CR26","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/S0036142999360044","volume":"38","author":"P Morin","year":"2000","unstructured":"Morin, P., Nochetto, R.H., Siebert, K.G.: Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 38(2), 466\u2013488 (2000). (electronic)","journal-title":"SIAM J. Numer. Anal."},{"key":"9912_CR27","doi-asserted-by":"crossref","unstructured":"Nochetto, R.H., Siebert, K.G., Veeser, A.: Theory of adaptive finite element methods: an introduction. In: Multiscale, Nonlinear and Adaptive Approximation, pp. 409\u2013542. Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-03413-8_12"},{"issue":"1","key":"9912_CR28","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0168-9274(99)00046-X","volume":"35","author":"A Schmidt","year":"2000","unstructured":"Schmidt, A., Siebert, K.G.: A posteriori estimators for the $$h$$ h - $$p$$ p version of the finite element method in 1D. Appl. Numer. Math. 35(1), 43\u201366 (2000)","journal-title":"Appl. Numer. Math."},{"issue":"2","key":"9912_CR29","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10208-005-0183-0","volume":"7","author":"R Stevenson","year":"2007","unstructured":"Stevenson, R.: Optimality of a standard adaptive finite element method. Found. Comput. Math. 7(2), 245\u2013269 (2007)","journal-title":"Found. Comput. Math."},{"key":"9912_CR30","doi-asserted-by":"crossref","unstructured":"Stevenson, R.: Adaptive wavelet methods for solving operator equations: an overview. In: Multiscale, Nonlinear and Adaptive Approximation, pp. 543\u2013597. Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-03413-8_13"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9912-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-014-9912-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9912-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T20:21:00Z","timestamp":1565814060000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-014-9912-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,10]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["9912"],"URL":"https:\/\/doi.org\/10.1007\/s10915-014-9912-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,10]]}}}