{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:45:23Z","timestamp":1776829523781,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"236","license":[{"start":{"date-parts":[[2001,4,19]],"date-time":"2001-04-19T00:00:00Z","timestamp":987638400000},"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>Tensor products of Gauss-Lobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if Gauss-Lobatto points exist in non-tensor-product domains like the simplex. In this work, we show that the <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n  <mml:semantics>\n    <mml:mi>n<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>-dimensional tensor-product of Gauss-Lobatto quadrature points are also Fekete points. This suggests a way to generalize spectral methods based on Gauss-Lobatto points to non-tensor-product domains, since Fekete points are known to exist and have been computed in the triangle and tetrahedron. In one dimension this result was proved by Fej\u00e9r in 1932, but the extension to higher dimensions in non-trivial.<\/p>","DOI":"10.1090\/s0025-5718-00-01262-x","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:13:53Z","timestamp":1027721633000},"page":"1543-1547","source":"Crossref","is-referenced-by-count":44,"title":["Tensor product Gauss-Lobatto points are Fekete points for the cube"],"prefix":"10.1090","volume":"70","author":[{"given":"L.","family":"Bos","sequence":"first","affiliation":[]},{"given":"M.","family":"Taylor","sequence":"additional","affiliation":[]},{"given":"B.","family":"Wingate","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,4,19]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/0021-9045(91)90063-G","article-title":"On certain configurations of points in \ud835\udc45\u207f which are unisolvent for polynomial interpolation","volume":"64","author":"Bos, L.","year":"1991","journal-title":"J. Approx. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9045","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"Chen, Q., and I. Babu\u0161ka, Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle,  Comput. Methods Appl. Mech. Engrg., 128, 405\u2013417, 1995.","DOI":"10.1016\/0045-7825(95)00889-6"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/BF01060030","article-title":"Spectral methods on triangles and other domains","volume":"6","author":"Dubiner, Moshe","year":"1991","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"key":"4","unstructured":"Fej\u00e9r, L., Bestimmung derjenigen Abszissen eines Intervalles f\u00fcr welche die Quadratsumme der Grundfunktionen der Lagrangeschen Interpolation im Intervalle [-1,1] ein m\u00f6glichst kleines Maximum besitzt, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mt. Ser. II, 1, 263\u2013276, 1932."},{"key":"5","doi-asserted-by":"crossref","unstructured":"Hesthaven, J. S., and C. H. Teng, Stable spectral methods on tetrahedral elements, SIAM J. Sci. Comput., 1999, in press.","DOI":"10.1137\/S1064827598343723"},{"key":"6","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix analysis","author":"Horn, Roger A.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0521305861"},{"key":"7","unstructured":"Komatitsch, D., et al., Wave propagation in 2-D elastic media using a spectral element method with triangles and quadrangles, submitted J. Comput. Acoust., 1999."},{"key":"8","unstructured":"Maday, Y. and A. T. Patera, Spectral element methods for the incompressible Navier-Stokes equations, in State of the Art Surveys in Computational Mechanics, edited by A. K. Noor, ASME, New York, 1988."},{"key":"9","doi-asserted-by":"crossref","unstructured":"Patera, A.T., A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys., 54, 468\u2013488, 1984.","DOI":"10.1016\/0021-9991(84)90128-1"},{"issue":"1-4","key":"10","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/0045-7825(94)00745-9","article-title":"A triangular spectral element method; applications to the incompressible Navier-Stokes equations","volume":"123","author":"Sherwin, S. J.","year":"1995","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"key":"11","unstructured":"Taylor, M. A., and B. A. Wingate, The Fekete collocation points for triangular spectral elements, SIAM J. Numer. Anal., 1998, submitted."},{"key":"12","unstructured":"Taylor, M. A., and B. A. Wingate, A generalized diagonal mass matrix spectral element method for non-quadrilateral elements, Appl. Num. Math., 1999, in press."},{"key":"13","unstructured":"Wingate, B. A., and J. P. Boyd, Spectral element methods on triangles for geophysical fluid dynamics problems, in Proceedings of the Third International Conference on Spectral and High-order Methods, edited by A. V. Ilin and L. R. Scott, pp. 305\u2013314, Houston J. Mathematics, Houston, Texas, 1996."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2001-70-236\/S0025-5718-00-01262-X\/S0025-5718-00-01262-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-236\/S0025-5718-00-01262-X\/S0025-5718-00-01262-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T00:37:36Z","timestamp":1627605456000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-236\/S0025-5718-00-01262-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4,19]]},"references-count":13,"journal-issue":{"issue":"236","published-print":{"date-parts":[[2001,10]]}},"alternative-id":["S0025-5718-00-01262-X"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-00-01262-x","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,4,19]]}}}