{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:24:19Z","timestamp":1777508659234,"version":"3.51.4"},"reference-count":62,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2110811"],"award-info":[{"award-number":["DMS-2110811"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2021-04311"],"award-info":[{"award-number":["RGPIN-2021-04311"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12301496"],"award-info":[{"award-number":["12301496"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters controlling the smoothness and the correlation length of the Gaussian random field. The proposed numerical method relies on the Balakrishnan integral representation of the solution and does not require the approximation of eigenpairs. Rather, it consists of a sinc quadrature coupled with a standard surface finite element method. We provide a complete error analysis of the method and illustrate its performances in several numerical experiments.<\/jats:p>","DOI":"10.1515\/cmam-2022-0237","type":"journal-article","created":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T10:23:39Z","timestamp":1704363819000},"page":"829-858","source":"Crossref","is-referenced-by-count":2,"title":["Numerical Approximation of Gaussian Random Fields on Closed Surfaces"],"prefix":"10.1515","volume":"24","author":[{"given":"Andrea","family":"Bonito","sequence":"first","affiliation":[{"name":"Department of Mathematics , Texas A&M University , College Station , TX 77843 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diane","family":"Guignard","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , University of Ottawa , Ottawa , ON K1N 6N5 , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3239-7124","authenticated-orcid":false,"given":"Wenyu","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , University of Electronic Science and Technology of China , No. 2006 Xiyuan Ave., West Hi-Tech Zone, 611731 , Chengdu , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,1,4]]},"reference":[{"key":"2024100217254136068_j_cmam-2022-0237_ref_001","unstructured":"R. J.  Adler and J. E.  Taylor,\nRandom Fields and Geometry,\nSpringer Monogr. Math.,\nSpringer, New York, 2007."},{"key":"2024100217254136068_j_cmam-2022-0237_ref_002","doi-asserted-by":"crossref","unstructured":"H.  Antil, J.  Pfefferer and S.  Rogovs,\nFractional operators with inhomogeneous boundary conditions: Analysis, control, and discretization,\nCommun. Math. Sci. 16 (2018), no. 5, 1395\u20131426.","DOI":"10.4310\/CMS.2018.v16.n5.a11"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_003","doi-asserted-by":"crossref","unstructured":"D.  Arndt, W.  Bangerth, M.  Feder, M.  Fehling, R.  Gassm\u00f6ller, T.  Heister, L.  Heltai, M.  Kronbichler, M.  Maier, P.  Munch, J.-P.  Pelteret, S.  Sticko, B.  Turcksin and D.  Wells,\nThe deal.II library, version 9.4,\nJ. Numer. 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Zouraris,\nGalerkin finite element approximations of stochastic elliptic partial differential equations,\nSIAM J. Numer. Anal. 42 (2004), no. 2, 800\u2013825.","DOI":"10.1137\/S0036142902418680"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_008","doi-asserted-by":"crossref","unstructured":"M.  Bachmayr and A.  Djurdjevac,\nMultilevel representations of isotropic Gaussian random fields on the sphere,\nIMA J. Numer. Anal. 43 (2023), no. 4, 1970\u20132000.","DOI":"10.1093\/imanum\/drac034"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_009","doi-asserted-by":"crossref","unstructured":"A. V.  Balakrishnan,\nFractional powers of closed operators and the semigroups generated by them,\nPacific J. Math. 10 (1960), 419\u2013437.","DOI":"10.2140\/pjm.1960.10.419"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_010","doi-asserted-by":"crossref","unstructured":"D.  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Trans. R. Soc. A 209 (1909), no. 441\u2013458, 415\u2013446.","DOI":"10.1098\/rsta.1909.0016"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_056","doi-asserted-by":"crossref","unstructured":"F.  Nobile and F.  Tesei,\nA multi level Monte Carlo method with control variate for elliptic PDEs with log-normal coefficients,\nStoch. Partial Differ. Equ. Anal. Comput. 3 (2015), no. 3, 398\u2013444.","DOI":"10.1007\/s40072-015-0055-9"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_057","doi-asserted-by":"crossref","unstructured":"C. E.  Rasmussen and C. K. I.  Williams,\nGaussian Processes for Machine Learning,\nAdapt. Comput. Mach. Learn.,\nMIT Press, Cambridge, 2006.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_058","doi-asserted-by":"crossref","unstructured":"C.  Schwab and R. A.  Todor,\nKarhunen\u2013Lo\u00e8ve approximation of random fields by generalized fast multipole methods,\nJ. Comput. Phys. 217 (2006), no. 1, 100\u2013122.","DOI":"10.1016\/j.jcp.2006.01.048"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_059","doi-asserted-by":"crossref","unstructured":"M. L.  Stein,\nInterpolation of Spatial Data: Some Theory for Kriging,\nSpringer Ser. Statist.,\nSpringer, New York, 1999.","DOI":"10.1007\/978-1-4612-1494-6"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_060","doi-asserted-by":"crossref","unstructured":"P.  Whittle,\nOn stationary processes in the plane,\nBiometrika 41 (1954), 434\u2013449.","DOI":"10.1093\/biomet\/41.3-4.434"},{"key":"2024100217254136068_j_cmam-2022-0237_ref_061","unstructured":"P.  Whittle,\nStochastic processes in several dimensions,\nBull. Inst. Internat. Statist. 40 (1963), 974\u2013994."},{"key":"2024100217254136068_j_cmam-2022-0237_ref_062","doi-asserted-by":"crossref","unstructured":"D.  Xiu and J. S.  Hesthaven,\nHigh-order collocation methods for differential equations with random inputs,\nSIAM J. Sci. 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