{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:47:19Z","timestamp":1776725239532,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"234","license":[{"start":{"date-parts":[[2001,3,1]],"date-time":"2001-03-01T00:00:00Z","timestamp":983404800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We analyze the Legendre and Chebyshev spectral Galerkin semidiscretizations of a one dimensional homogeneous parabolic problem with nonconstant coefficients. We present error estimates for both smooth and nonsmooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we find an arbitrary high order of convegence.<\/p>","DOI":"10.1090\/s0025-5718-00-01195-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:46Z","timestamp":1027707466000},"page":"525-531","source":"Crossref","is-referenced-by-count":0,"title":["On error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth initial data"],"prefix":"10.1090","volume":"70","author":[{"given":"Javier","family":"de Frutos","sequence":"first","affiliation":[]},{"given":"Rafael","family":"Mu\u00f1oz-Sola","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,3,1]]},"reference":[{"key":"1","series-title":"Grundlehren der Mathematischen Wissenschaften, No. 223","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66451-9","volume-title":"Interpolation spaces. An introduction","author":"Bergh, J\u00f6ran","year":"1976"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1137\/0726045","article-title":"Properties of some weighted Sobolev spaces and application to spectral approximations","volume":"26","author":"Bernardi, Christine","year":"1989","journal-title":"SIAM J. Numer. 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[Collection of the Atomic Energy Commission: Science Series]","isbn-type":"print","volume-title":"Analyse math\\'{e}matique et calcul num\\'{e}rique pour les sciences et les techniques. Tome 2","author":"Dautray, Robert","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/222580513X"},{"key":"6","unstructured":"J. de Frutos and R. Mu\u00f1oz Sola, Chebyshev pseudospectral collocation for parabolic problems with nonconstant coefficients, Proceedings of the third international conference on spectral and high order methods, Houston (Texas), 1996, 101-107."},{"key":"7","unstructured":"J. de Frutos and R. Mu\u00f1oz Sola, Error estimates for Galerkin spectral discretizations of parabolic problems with nonsmooth data, Applied Mathematics and Computation Reports 1998\/7, Universidad de Valladolid (Spain), pp. 749\u2013754."},{"key":"8","unstructured":"G. Fern\u00e1ndez Man\u00edn. Algunas contribuciones al estudio del error en los m\u00e9todos espectrales: optimalidad de los m\u00e9todos de Jacobi y estudio del m\u00e9todo de \u201cpatching\". PhD Thesis. Santiago de Compostela, 1995."},{"key":"9","isbn-type":"print","volume-title":"III Congreso de Matem\\'{a}tica Aplicada\/XIII C.E.D.Y.A. (Congreso de Ecuaciones Diferenciales y Aplicaciones)","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/8460532739"},{"key":"10","series-title":"Handbook of Numerical Analysis, II","isbn-type":"print","volume-title":"Handbook of numerical analysis. Vol. II","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0444703659"},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1137\/0719003","article-title":"On the smoothing property of the Galerkin method for parabolic equations","volume":"19","author":"Luskin, Mitchell","year":"1982","journal-title":"SIAM J. Numer. 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