{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T21:56:43Z","timestamp":1768773403069,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2013,5]]},"DOI":"10.1007\/s10915-012-9633-4","type":"journal-article","created":{"date-parts":[[2012,8,31]],"date-time":"2012-08-31T08:56:17Z","timestamp":1346403377000},"page":"327-350","source":"Crossref","is-referenced-by-count":5,"title":["Generalized Jacobi Approximation in Multiple Dimensions and Its Applications"],"prefix":"10.1007","volume":"55","author":[{"given":"Tao","family":"Sun","sequence":"first","affiliation":[]},{"given":"Ben-yu","family":"Guo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,9,1]]},"reference":[{"key":"9633_CR1","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1137\/S0036142901356551","volume":"39","author":"I. Babus\u0306ka","year":"2001","unstructured":"Babus\u0306ka, I., Guo, B.Q.: Direct and inverse approximation theorems for the p-version of finite element method in the framework of weighted Besov spaces, Part I: approximability of functions in the weighted Besov space. SIAM J. Numer. Anal. 39, 1512\u20131538 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR2","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1137\/S0036142999359670","volume":"38","author":"Z. Belhachmi","year":"2001","unstructured":"Belhachmi, Z., Bernardi, C., Karageorghis, A.: Spectral element discretization of the circular driven cavity, Part II: the bilaplacian equation. SIAM J. Numer. Anal. 38, 1926\u20131960 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR3","series-title":"Series in Applied Mathematics","volume-title":"Spectral Methods for Axisymmetric Domains","author":"C. Bernardi","year":"1999","unstructured":"Bernardi, C., Dauge, M., Maday, Y.: In: Ciarlet, P.G., Lions, P.L. (eds.) Spectral Methods for Axisymmetric Domains. Series in Applied Mathematics, vol. 3. Gauhtier-Villars & North-Holland, Paris (1999)"},{"key":"9633_CR4","first-page":"209","volume-title":"Handbook of Numerical Analysis, Techniques of Scientific Computing","author":"C. Bernardi","year":"1997","unstructured":"Bernardi, C., Maday, Y.: Spectral methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, Techniques of Scientific Computing, vol. 5, pp. 209\u2013486. Elsevier, Amsterdam (1997)"},{"key":"9633_CR5","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1137\/S1064827598342407","volume":"22","author":"B. Bialecki","year":"2000","unstructured":"Bialecki, B., Karageorghis, A.: A Legendre spectral Galerkin method for the biharmonic Dirichlet problem. SIAM J. Sci. Comput. 22, 1549\u20131569 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"9633_CR6","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1137\/S1064827596298233","volume":"18","author":"P.E. Bj\u00f8rstad","year":"1997","unstructured":"Bj\u00f8rstad, P.E., Tj\u00f8stheim, B.P.: Efficient algorithms for solving a fourth-order equation with spectral-Galerkin method. SIAM J. Sci. Comput. 18, 621\u2013632 (1997)","journal-title":"SIAM J. Sci. Comput."},{"key":"9633_CR7","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/0021-9991(87)90158-6","volume":"69","author":"J.P. Boyd","year":"1987","unstructured":"Boyd, J.P.: Spectral methods using rational basis functions on an infinite interval. J.\u00a0Comput. Phys. 69, 112\u2013142 (1987)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9633_CR8","volume-title":"Chebyshev and Fourier Spectral Methods","author":"J.P. Boyd","year":"2001","unstructured":"Boyd, J.P.: Chebyshev and Fourier Spectral Methods, 2nd edn. Dover, Mineola (2001)","edition":"2"},{"key":"9633_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-30726-6","volume-title":"Spectral Methods, Fundamentals in Single Domains","author":"C. Canuto","year":"2006","unstructured":"Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods, Fundamentals in Single Domains. Springer, Berlin (2006)"},{"key":"9633_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-30728-0","volume-title":"Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics","author":"C. Canuto","year":"2007","unstructured":"Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer, Berlin (2007)"},{"key":"9633_CR11","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1016\/j.apnum.2007.07.001","volume":"58","author":"E.H. Doha","year":"2008","unstructured":"Doha, E.H., Bhrawy, A.H.: Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials. Appl. Numer. Math. 58, 1224\u20131244 (2008)","journal-title":"Appl. Numer. Math."},{"key":"9633_CR12","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF01060030","volume":"6","author":"M. Dubiner","year":"1991","unstructured":"Dubiner, M.: Spectral methods on triangles and other domains. J. Sci. Comput. 6, 345\u2013390 (1991)","journal-title":"J. Sci. Comput."},{"key":"9633_CR13","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970425","volume-title":"Numerical Analysis of Spectral Methods: Theory and Applications","author":"D. Gottlieb","year":"1977","unstructured":"Gottlieb, D., Orszag, S.A.: Numerical Analysis of Spectral Methods: Theory and Applications. SIAM-CBMS, Philadelphia (1977)"},{"key":"9633_CR14","doi-asserted-by":"crossref","DOI":"10.1142\/9789812816641","volume-title":"Spectral Methods and Their Applications","author":"B.-y. Guo","year":"1998","unstructured":"Guo, B.-y.: Spectral Methods and Their Applications. World Scientific, Singapore (1998)"},{"key":"9633_CR15","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1006\/jmaa.1998.6025","volume":"226","author":"B.-y. Guo","year":"1998","unstructured":"Guo, B.-y.: Gegenbauer approximation and its applications to differential equations on the whole line. J.\u00a0Math. Anal. Appl. 226, 180\u2013206 (1998)","journal-title":"J.\u00a0Math. Anal. Appl."},{"key":"9633_CR16","first-page":"95","volume":"18","author":"B.-y. Guo","year":"2000","unstructured":"Guo, B.-y.: Jacobi spectral approximation and its applications to differential equations on the half line. J.\u00a0Comput. Math. 18, 95\u2013112 (2000)","journal-title":"J.\u00a0Comput. Math."},{"key":"9633_CR17","first-page":"621","volume":"37","author":"B.-y. Guo","year":"2000","unstructured":"Guo, B.-y.: Gegenbauer approximation in certain Hilbert spaces and its applications to singular differential equations on the whole line. SIAM J. Numer. Anal. 37, 621\u2013645 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR18","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1006\/jmaa.1999.6677","volume":"243","author":"B.-y. Guo","year":"2000","unstructured":"Guo, B.-y.: Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations. J. Math. Anal. Appl. 243, 373\u2013408 (2000)","journal-title":"J. Math. Anal. Appl."},{"key":"9633_CR19","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1137\/S0036142996297084","volume":"35","author":"B.-y. Guo","year":"1998","unstructured":"Guo, B.-y., He, L.-p.: The fully discrete Legendre spectral approximation of two-dimensional unsteady incompressible fluid flow in stream function form. SIAM J. Numer. Anal. 35, 146\u2013176 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR20","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1090\/S0025-5718-10-02329-X","volume":"79","author":"B.-y. Guo","year":"2010","unstructured":"Guo, B.-y., Jia, H.-l.: Spectral method on quadrilaterals. Math. Comput. 79, 2237\u20132264 (2010)","journal-title":"Math. Comput."},{"key":"9633_CR21","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s10444-006-9020-5","volume":"28","author":"B.-y. Guo","year":"2008","unstructured":"Guo, B.-y., Shen, J.: Irrational approximations and their applications to partial differential equations in exterior domains. Adv. Comput. Math. 28, 237\u2013267 (2008)","journal-title":"Adv. Comput. Math."},{"key":"9633_CR22","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1512\/iumj.2001.50.2090","volume":"50","author":"B.-y. Guo","year":"2001","unstructured":"Guo, B.-y., Shen, J.: On spectral approximations using modified Legendre rational functions: application to the Korteweg de Vries equation on the half line. Indiana Univ. Math. J. 50, 181\u2013204 (2001)","journal-title":"Indiana Univ. Math. J."},{"key":"9633_CR23","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s10915-005-9055-7","volume":"27","author":"B.-y. Guo","year":"2006","unstructured":"Guo, B.-y., Shen, J., Wang, L.-l.: Optimal spectral-Galerkin methods using generalized Jacobi polynomials. J. Sci. Comput. 27, 305\u2013322 (2006)","journal-title":"J. Sci. Comput."},{"key":"9633_CR24","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1016\/j.apnum.2008.04.003","volume":"59","author":"B.-y. Guo","year":"2009","unstructured":"Guo, B.-y., Shen, J., Wang, L.-l.: Generalized Jacobi polynomials\/Functions and their applications. Appl. Numer. Math. 59, 1011\u20131028 (2009)","journal-title":"Appl. Numer. Math."},{"key":"9633_CR25","author":"B.-y. Guo","year":"2012","unstructured":"Guo, B.-y., Sun, T., Zhang, C.: Jacobi and Laguerre quasi-orthogonal approximations and related interpolations. Math. Comp. (2012). doi: 10.1090\/S0025-5718-2012-02614-7","journal-title":"Math. Comp."},{"key":"9633_CR26","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10444-005-7471-8","volume":"26","author":"B.-y. Guo","year":"2007","unstructured":"Guo, B.-y., Wang, L.-l.: Error analysis of spectral method on a triangle. Adv. Comput. Math. 26, 473\u2013496 (2007)","journal-title":"Adv. Comput. Math."},{"key":"9633_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jat.2004.03.008","volume":"28","author":"B.-y. Guo","year":"2004","unstructured":"Guo, B.-y., Wang, L.-l.: Jacobi approximations and Jacobi-Gauss-type interpolations in non-uniformly Jacobi-weighted Sobolev spaces. J. Approx. Theory 28, 1\u201341 (2004)","journal-title":"J. Approx. Theory"},{"key":"9633_CR28","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s10915-010-9367-0","volume":"44","author":"B.-y. Guo","year":"2010","unstructured":"Guo, B.-y., Wang, T.-j.: Composite Laguerre-Legendre spectral method for fourth order exterior problems. J. Sci. Comput. 44, 255\u2013285 (2010)","journal-title":"J. Sci. Comput."},{"issue":"Suppl.","key":"9633_CR29","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1360\/04za0014","volume":"47","author":"B.-y. Guo","year":"2004","unstructured":"Guo, B.-y., Wang, Z.-q.: Legendre rational approximation on the whole line. Sci. China Ser. A 47(Suppl.), 155\u2013164 (2004)","journal-title":"Sci. China Ser. A"},{"key":"9633_CR30","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.apnum.2005.01.002","volume":"55","author":"B.-y. Guo","year":"2005","unstructured":"Guo, B.-y., Wang, Z.-q., Wan, Z.-s., Chu, D.: Second order Jacobi approximation with applications to fourth order differential equations. Appl. Numer. Math. 55, 480\u2013502 (2005)","journal-title":"Appl. Numer. Math."},{"key":"9633_CR31","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10915-010-9353-6","volume":"43","author":"B.-y. Guo","year":"2010","unstructured":"Guo, B.-y., Yi, Y.-g.: Generalized Jacobi rational spectral method and its applications. J. Sci. Comput. 43, 201\u2013238 (2010)","journal-title":"J. Sci. Comput."},{"key":"9633_CR32","series-title":"Lecture Notes in Computational Sciences and Engineering","first-page":"237","volume-title":"Proceeding od for the International Conference on Spectral and High-Order Methods (ICOSAHOMO09)","author":"Y.-y. Li","year":"2010","unstructured":"Li, Y.-y., Wang, L.-L., Li, H.-y., Ma, H.-p.: A new spectral method on triangles. In: Proceeding od for the International Conference on Spectral and High-Order Methods (ICOSAHOMO09). Lecture Notes in Computational Sciences and Engineering, pp. 237\u2013246. Springer, Berlin (2010)"},{"key":"9633_CR33","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1137\/S0036142999361505","volume":"38","author":"H. Ma","year":"2000","unstructured":"Ma, H., Sun, W.: A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations. SIAM J. Numer. Anal. 38, 1425\u20131438 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR34","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1137\/S0036142900378327","volume":"39","author":"H. Ma","year":"2001","unstructured":"Ma, H., Sun, W.: Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation. SIAM J. Numer. Anal. 39, 1380\u20131394 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR35","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1098\/rspa.1998.0189","volume":"454","author":"R.G. Owens","year":"1998","unstructured":"Owens, R.G.: Spectral approximation on the triangle. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 454, 857\u2013872 (1998)","journal-title":"Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci."},{"key":"9633_CR36","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1137\/0915089","volume":"15","author":"J. Shen","year":"1994","unstructured":"Shen, J.: Efficient spectral-Galerkin method, I. Direct solvers of second- and fourth-order equations using Legendre polynomials. SIAM J. Sci. Comput. 15, 1489\u20131505 (1994)","journal-title":"SIAM J. Sci. Comput."},{"key":"9633_CR37","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1137\/070702023","volume":"47","author":"J. Shen","year":"2009","unstructured":"Shen, J., Wang, L.-l., Li, H.-y.: A triangular spectral element method using fully tensorial rational basis functions. SIAM J. Numer. Anal. 47, 1619\u20131650 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"9633_CR38","doi-asserted-by":"crossref","first-page":"3775","DOI":"10.1002\/nme.1620382204","volume":"38","author":"S.J. Sherwin","year":"1995","unstructured":"Sherwin, S.J., Karniadakis, G.E.: A new triangular and tetrahedral basis for high-order finite element methods. Int. J. Numer. Methods Eng. 38, 3775\u20133802 (1995)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"9633_CR39","volume-title":"Orthogonal Polynomials","author":"G. Szeg\u00f6","year":"1959","unstructured":"Szeg\u00f6, G.: Orthogonal Polynomials. Amer. Math. Soc., Providence (1959)"},{"key":"9633_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10444-011-9193-4","volume":"37","author":"Y.-g. Yi","year":"2012","unstructured":"Yi, Y.-g., Guo, B.-y.: Generalized Jacobi rational spectral method on the half line. Adv. Comput. Math. 37, 1\u201337 (2012)","journal-title":"Adv. Comput. Math."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-012-9633-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-012-9633-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-012-9633-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,3]],"date-time":"2019-07-03T08:05:19Z","timestamp":1562141119000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-012-9633-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,1]]},"references-count":40,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["9633"],"URL":"https:\/\/doi.org\/10.1007\/s10915-012-9633-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9,1]]}}}