{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,16]],"date-time":"2024-01-16T09:37:10Z","timestamp":1705397830835},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2017,2,4]],"date-time":"2017-02-04T00:00:00Z","timestamp":1486166400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s10444-017-9513-4","type":"journal-article","created":{"date-parts":[[2017,2,4]],"date-time":"2017-02-04T04:34:01Z","timestamp":1486182841000},"page":"973-998","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A fast discrete spectral method for stochastic partial differential equations"],"prefix":"10.1007","volume":"43","author":[{"given":"Yanzhao","family":"Cao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuesheng","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,2,4]]},"reference":[{"key":"9513_CR1","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1137\/050645142","volume":"45","author":"I Babu\u0161ka","year":"2007","unstructured":"Babu\u0161ka, I., Nobile, F., Tempone, R.: A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 45, 1005\u20131034 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR2","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1137\/100786356","volume":"52","author":"I Babu\u0161ka","year":"2010","unstructured":"Babu\u0161ka, I., Nobile, F., Tempone, R.: A stochastic collocation method for elliptic partial differential equations with random input data. SIAM Rev. 52, 317\u2013355 (2010)","journal-title":"SIAM Rev."},{"key":"9513_CR3","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1137\/S0036142902418680","volume":"42","author":"I Babu\u0161ka","year":"2004","unstructured":"Babu\u0161ka, I., Tempone, R., Zouraris, G.E.: Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42, 800\u2013825 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR4","first-page":"211","volume":"52","author":"E Barletta","year":"2009","unstructured":"Barletta, E., Dragomir, S.: Vector valued holomorphic functions. Bull. Math. Soc. Sci. Math. Roumanie 52, 211\u2013226 (2009)","journal-title":"Bull. Math. Soc. Sci. Math. Roumanie"},{"key":"9513_CR5","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1023\/A:1018977404843","volume":"2","author":"V Barthelmann","year":"2000","unstructured":"Barthelmann, V., Novak, E., Ritter, E.: High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 2, 273\u2013288 (2000)","journal-title":"Adv. Comput. Math."},{"key":"9513_CR6","volume-title":"Stochastic spectral galerkin and collocation methods for pdes with random coefficients: A numerical comparison, in Lecture Notes in Computational Science and Engineering","author":"J B\u00e4ck","year":"2011","unstructured":"B\u00e4ck, J., Nobile, F., Tamellini, L., Tempone, R.: Stochastic spectral galerkin and collocation methods for pdes with random coefficients: A numerical comparison, in Lecture Notes in Computational Science and Engineering. Springer, New York (2011)"},{"key":"9513_CR7","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s00211-011-0377-0","volume":"119","author":"A Barth","year":"2001","unstructured":"Barth, A., Schwab, C., Zollinger, N.: Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients. Numer. Math. 119, 123\u2013161 (2001)","journal-title":"Numer. Math."},{"key":"9513_CR8","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1016\/j.cma.2008.08.019","volume":"198","author":"M Bieri","year":"2009","unstructured":"Bieri, M., Schwab, C.: Sparse high order FEM for elliptic SPDEs. Comput. Methods Appl. Mech. Engrg. 198, 1149\u20131170 (2009)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"9513_CR9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.laa.2009.08.002","volume":"432","author":"A Bostan","year":"2010","unstructured":"Bostan, A., Salvy, B., Schost, \u00c9.: Fast conversion algorithms for orthogonal polynomials. Linear Algebra Appl. 432, 249\u2013258 (2010)","journal-title":"Linear Algebra Appl."},{"key":"9513_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","author":"SC Brenner","year":"2008","unstructured":"Brenner, S.C., Scott, L.R.: The mathematical theory of finite element methods, 3rd edn. Springer, New York (2008)","edition":"3rd edn."},{"key":"9513_CR11","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/j.jco.2014.02.001","volume":"30","author":"Y Cao","year":"2014","unstructured":"Cao, Y., Jiang, Y., Xu, Y.: A fast algorithm for orthogonal polynomial expansions on sparse grids. J. Complex. 30, 673\u2013682 (2014)","journal-title":"J. Complex."},{"key":"9513_CR12","doi-asserted-by":"crossref","first-page":"607","DOI":"10.3934\/cpaa.2007.6.607","volume":"6","author":"Y Cao","year":"2007","unstructured":"Cao, Y., Yin, L.: Spectral Galerkin method for stochastic wave equations driven by space-time white noise. Commun. Pure Appl. Anal. 6, 607\u2013617 (2007)","journal-title":"Commun. Pure Appl. Anal."},{"key":"9513_CR13","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1090\/S0025-5718-2011-02513-5","volume":"81","author":"A Chernov","year":"2012","unstructured":"Chernov, A.: Optimal convergence estimates for the trace of the polynomial L 2-projection operator on a simplex. Math. Comp. 81, 765\u2013787 (2012)","journal-title":"Math. Comp."},{"key":"9513_CR14","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1090\/S0025-5718-2013-02692-0","volume":"82","author":"A Chernov","year":"2013","unstructured":"Chernov, A., Schwab, C.: First order k-th moment finite element analysis of nonlinear operator equations with stochastic data. Math. Comp. 82, 1859\u20131888 (2013)","journal-title":"Math. Comp."},{"key":"9513_CR15","volume-title":"The finite element method for elliptic problems, in Studies in Mathematics and its Applications","author":"PG Ciarlet","year":"1978","unstructured":"Ciarlet, P.G.: The finite element method for elliptic problems, in Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam (1978)"},{"key":"9513_CR16","first-page":"2736","volume":"5","author":"G Cuypers","year":"2004","unstructured":"Cuypers, G., Ysebaert, G., Moonen, M., Pisoni, F.: Chebyshev interpolation for dmt modems. IEEE Int. Conf. 5, 2736\u20132740 (2004)","journal-title":"IEEE Int. Conf."},{"key":"9513_CR17","doi-asserted-by":"crossref","first-page":"483","DOI":"10.3233\/IDA-2002-6602","volume":"6","author":"J Garcke","year":"2002","unstructured":"Garcke, J., Griebel, M.: Classification with anisotropic sparse grids using simplicial basis functions. Intell. Data Anal. 6, 483\u2013502 (2002)","journal-title":"Intell. Data Anal."},{"key":"9513_CR18","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00607-003-0015-5","volume":"71","author":"T Gerstner","year":"2003","unstructured":"Gerstner, T., Griebel, M.: Dimension-adaptive tensor-product quadrature. Computing 71, 65\u201387 (2003)","journal-title":"Computing"},{"key":"9513_CR19","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717822","volume-title":"Numerical methods for special functions","author":"A Gil","year":"2007","unstructured":"Gil, A., Segura, J., Temme, N.M.: Numerical methods for special functions. SIAM, Philadelphia, PA (2007)"},{"key":"9513_CR20","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/978-3-319-04537-5_6","volume":"97","author":"M Gunzburger","year":"2014","unstructured":"Gunzburger, M., Zhang, G., Webster, C.: An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data. Lect. Notes Comput. Sci. Eng. 97, 137\u2013170 (2014)","journal-title":"Lect. Notes Comput. Sci. Eng."},{"key":"9513_CR21","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1137\/050654141","volume":"46","author":"E Hausenblas","year":"2008","unstructured":"Hausenblas, E.: Finite element approximation of stochastic partial differential equations driven by Poisson random measures of jump type. SIAM J. Numer. Anal. 46, 437\u2013471 (2008)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR22","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s10543-014-0511-3","volume":"55","author":"N Collier","year":"2015","unstructured":"Collier, N., Haji-Ali, A.L., Nobile, F., von Schwerin, E., Tempone, R.: A continuation multi level Monte Carlo algorithm. BIT Numer. Math. 55, 399\u2013432 (2015)","journal-title":"BIT Numer. Math."},{"issue":"1","key":"9513_CR23","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.jco.2009.10.001","volume":"26","author":"Y Jiang","year":"2010","unstructured":"Jiang, Y., Xu, Y.: Fast discrete algorithms for sparse fourier exnpansions fo high dimensional functions. J. Complex. 26(1), 51\u201381 (2010)","journal-title":"J. Complex."},{"key":"9513_CR24","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.jco.2011.03.003","volume":"27","author":"Y Jiang","year":"2011","unstructured":"Jiang, Y., Xu, Y.: B-spline quasi-interpolation on sparse grids. J. Complex. 27, 466\u2013488 (2011)","journal-title":"J. Complex."},{"key":"9513_CR25","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.1090\/S0025-5718-2014-02785-3","volume":"83","author":"Y Jiang","year":"2014","unstructured":"Jiang, Y., Xu, Y.: Fast computation of the multidimensional discrete fourier transform and inverse fourier transform on sparse grids. Math. Comp. 83, 2347\u20132384 (2014)","journal-title":"Math. Comp."},{"key":"9513_CR26","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1137\/100785715","volume":"33","author":"BN Khoromskij","year":"2011","unstructured":"Khoromskij, B.N., Schwab, C.: Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. SIAM J. Sci. Comput. 33, 364\u2013385 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"9513_CR27","first-page":"419","volume":"14","author":"G Migliorati","year":"2014","unstructured":"Migliorati, G., Nobile, F., Schwerin, E., Tempone, R.: Analysis of the discrete L 2 projection on polynomial spaces with random evaluations. Found. Comput. Math. 14, 419\u2013456 (2014)","journal-title":"Found. Comput. Math."},{"key":"9513_CR28","doi-asserted-by":"crossref","first-page":"2411","DOI":"10.1137\/070680540","volume":"46","author":"F Nobile","year":"2008","unstructured":"Nobile, F., Tempone, R., Webster, C.G.: An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. 46, 2411\u20132442 (2008)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR29","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1137\/060663660","volume":"46","author":"F Nobile","year":"2008","unstructured":"Nobile, F., Tempone, R., Webster, C.G.: A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. 46, 2309\u20132345 (2008)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR30","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1137\/090765547","volume":"48","author":"J Shen","year":"2010","unstructured":"Shen, J., Wang, L.: Sparse spectral approximations of high-dimensional problems based on hyperbolic cross. SIAM J. Numer. Anal. 48, 1087\u20131109 (2010)","journal-title":"SIAM J. Numer. Anal."},{"key":"9513_CR31","doi-asserted-by":"crossref","first-page":"3228","DOI":"10.1137\/100787842","volume":"32","author":"J Shen","year":"2010","unstructured":"Shen, J., Yu, H.: Efficient spectral sparse grid methods and applications to high-dimensional elliptic problems. SIAM J. Sci. Comput. 32, 3228\u20133250 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"9513_CR32","unstructured":"Strang, G., Fix, G.J.: An analysis of the finite element method, prentice-hall series in automatic computation, 2nd edn. Wellesley-Cambridge Press (2008)"},{"key":"9513_CR33","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.1137\/140961894","volume":"36","author":"T Tang","year":"2014","unstructured":"Tang, T., Zhou, T.: On discrete least-squares projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification. SIAM J. Sci. Comput. 36, 2272\u20132295 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"9513_CR34","unstructured":"Teckentrup, A., Jantsch, P., Webster, C., Gunzburger, M.: A multilevel stochastic collocation method for partial differential equations with random input data, arXiv preprint arXiv: 128.84.21.199 (2014)"},{"key":"9513_CR35","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1093\/imanum\/drl025","volume":"27","author":"RA Todor","year":"2007","unstructured":"Todor, R.A., Schwab, C.: Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. IMA J. Numer. Anal. 27, 232\u2013261 (2007)","journal-title":"IMA J. Numer. Anal."},{"key":"9513_CR36","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1137\/S106482750342684X","volume":"26","author":"X Wan","year":"2004","unstructured":"Wan, X., Xiu, D., Karniadakis, G.E.: Stochastic solutions for the two-dimensional advection-diffusion equation. SIAM J. Sci. Comput. 26, 578\u2013590 (2004)","journal-title":"SIAM J. Sci. Comput."},{"key":"9513_CR37","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1137\/S1064827501387826","volume":"24","author":"D Xiu","year":"2002","unstructured":"Xiu, D., Karniadakis, G.E.: The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24, 619\u2013644 (2002)","journal-title":"SIAM J. Sci. Comput."},{"key":"9513_CR38","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0021-9991(03)00092-5","volume":"187","author":"D Xiu","year":"2003","unstructured":"Xiu, D., Karniadakis, G.E.: Modeling uncertainty in flow simulations via generalized polynomial chaos. J. Comput. Phys. 187, 137\u2013167 (2003)","journal-title":"J. Comput. Phys."},{"key":"9513_CR39","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.jcp.2008.09.008","volume":"228","author":"D Xiu","year":"2009","unstructured":"Xiu, D., Shen, J.: Efficient stochastic Galerkin methods for random diffusion equations. J. Comput. Phys. 228, 266\u2013281 (2009)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-017-9513-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-017-9513-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-017-9513-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T03:50:31Z","timestamp":1568778631000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-017-9513-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,4]]},"references-count":39,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["9513"],"URL":"https:\/\/doi.org\/10.1007\/s10444-017-9513-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,4]]}}}