{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T19:18:34Z","timestamp":1774379914888,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2006,8,9]],"date-time":"2006-08-09T00:00:00Z","timestamp":1155081600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2007,3,16]]},"DOI":"10.1007\/s10444-005-7471-8","type":"journal-article","created":{"date-parts":[[2006,8,11]],"date-time":"2006-08-11T08:15:08Z","timestamp":1155284108000},"page":"473-496","source":"Crossref","is-referenced-by-count":18,"title":["Error analysis of spectral method on a triangle"],"prefix":"10.1007","volume":"26","author":[{"given":"Ben-yu","family":"Guo","sequence":"first","affiliation":[]},{"given":"Li-Lian","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,8,9]]},"reference":[{"key":"7471_CR1","volume-title":"Functions hyperg\u00e9om\u00e9triques et hyperspheriques-polynomes d'Hermite","author":"P. Appell","year":"1926","unstructured":"P. Appell and J. Kamp\u00e9 de F\u00e9riet, Functions hyperg\u00e9om\u00e9triques et hyperspheriques-polynomes d'Hermite (Gauthier-Villars, Paris, 1926)."},{"key":"7471_CR2","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/PL00005387","volume":"85","author":"I. Babu\u0161ka","year":"2000","unstructured":"I. Babu\u0161ka and B.Q. Guo, Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two-dimensions, Numer. Math. 85 (2000) 219\u2013255.","journal-title":"Numer. Math."},{"key":"7471_CR3","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1137\/S0036142901356551","volume":"39","author":"I. Babu\u0161ka","year":"2001","unstructured":"I. Babu\u0161ka and B.Q. Guo, Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spacecs, part I, approximability of functions in weighted Besov spaces, SIAM J. Numer. Anal. 39 (2001) 1512\u20131538.","journal-title":"SIAM J. Numer. Anal."},{"key":"7471_CR4","volume-title":"Handbook of Numerical Analysis, Part 5","author":"C. Bernardi","year":"1977","unstructured":"C. Bernardi and Y. Maday, Spectral method, in: Handbook of Numerical Analysis, Part 5, eds. P.G. Ciarlet and J.L. Lions (North-Holland, Amsterdam, 1977)."},{"key":"7471_CR5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1023\/A:1025624822162","volume":"14","author":"W. Cai","year":"1999","unstructured":"W. Cai, High-order mixed current bais functions for electromagnetic scattering of curve surface, J. Sci. Comput. 14 (1999) 73\u2013105.","journal-title":"J. Sci. Comput."},{"key":"7471_CR6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1090\/S0025-5718-1982-0637287-3","volume":"38","author":"C. Canuto","year":"1982","unstructured":"C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp. 38 (1982) 67\u201386.","journal-title":"Math. Comp."},{"key":"7471_CR7","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF01060030","volume":"6","author":"M. Dubiner","year":"1991","unstructured":"M. Dubiner, Spectral methods on triangles and other domains, J. Sci. Comput. 6 (1991) 345\u2013390.","journal-title":"J. Sci. Comput."},{"key":"7471_CR8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511565717","volume-title":"Orthogonal Polynomials of Several Variables","author":"C.F. Dunkl","year":"2001","unstructured":"C.F. Dunkl and Y. Xu, Orthogonal Polynomials of Several Variables (Cambridge Univ. Press, Cambridge, 2001)."},{"key":"7471_CR9","first-page":"121","volume":"42","author":"D. Funaro","year":"1991","unstructured":"D. Funaro, Pseudospectral approximation of a PDE defined on a triangle, Appl. Math. Comput. 42 (1991) 121\u2013138.","journal-title":"Appl. Math. Comput."},{"key":"7471_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-46783-0","volume-title":"Polynomial Approximations of Differential Equations","author":"D. Funaro","year":"1992","unstructured":"D. Funaro, Polynomial Approximations of Differential Equations (Springer-Verlag, Berlin, 1992)."},{"key":"7471_CR11","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1006\/jmaa.1999.6677","volume":"243","author":"B.-y. Guo","year":"2000","unstructured":"B.-y. Guo, Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations, J. Math. Anal. Appl. 243 (2000) 373\u2013408.","journal-title":"J. Math. Anal. Appl."},{"key":"7471_CR12","first-page":"157","volume-title":"Contemporary Mathematics, Vol. 329","author":"B.-y. Guo","year":"2003","unstructured":"B.-y. Guo and L.-L. Wang, Non-isotropic Jacobi spectral method, in: Contemporary Mathematics, Vol. 329 (Amer. Math. Soc., Providence, RI, 2003) pp. 157\u2013169."},{"key":"7471_CR13","volume-title":"Inequalities","author":"G.H. Hardy","year":"1952","unstructured":"G.H. Hardy, J.E. Littlewood and G. P\u00f3lya, Inequalities (Cambridge Univ. Press, Cambridge, 1952)."},{"key":"7471_CR14","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1006\/jcph.1998.6052","volume":"145","author":"W. Heinrichs","year":"1998","unstructured":"W. Heinrichs, Spectral collocation on triangular elements, J. Comput. Phys. 145 (1998) 743\u2013757.","journal-title":"J. Comput. Phys."},{"key":"7471_CR15","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/S0045-7825(98)00361-2","volume":"175","author":"J.S. Hesthaven","year":"1999","unstructured":"J.S. Hesthaven and D. Gottlieb, Stable spectral methods for conservation law on triangles with unstructured grids, Comput. Methods Appl. Mech. Engrg. 175 (1999) 361\u2013381.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7471_CR16","volume-title":"Spectral\/hp Element Methods for CFD","author":"G.E. Karniadakis","year":"1999","unstructured":"G.E. Karniadakis and S.J. Sherwin, Spectral\/hp Element Methods for CFD (Oxford Univ. Press, Oxford, 1999)."},{"key":"7471_CR17","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1098\/rspa.1998.0189","volume":"454","author":"R.G. Owens","year":"1998","unstructured":"R.G. Owens, Spectral Approximation on the triangle, Proc. Roy. Soc. London A 454 (1998) 857\u2013872.","journal-title":"Proc. Roy. Soc. London A"},{"key":"7471_CR18","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1002\/nme.1620382204","volume":"38","author":"S.J. Sherwin","year":"1995","unstructured":"S.J. Sherwin and G.E. Farniadakis, A new triangular and tetrahedral basis for high-order finite element methods, Internat. J. Numer. Methods Engrg. 38 (1995) 3775\u20133802.","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"7471_CR19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0045-7825(94)00745-9","volume":"123","author":"S.J. Sherwin","year":"1995","unstructured":"S.J. Sherwin and G.E. Farniadakis, A triangular spetral element method: applications to the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 123 (1995) 189\u2013229.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"7471_CR20","unstructured":"G. Szeg\u00f6, Othogonal Polynomials, Vol. 23, 4th edn. (AWS Coll. Publ., 1975)."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-005-7471-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-005-7471-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-005-7471-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T21:49:00Z","timestamp":1587160140000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-005-7471-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,9]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,3,16]]}},"alternative-id":["7471"],"URL":"https:\/\/doi.org\/10.1007\/s10444-005-7471-8","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,8,9]]}}}