{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T16:17:36Z","timestamp":1778689056076,"version":"3.51.4"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:00:00Z","timestamp":1774310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:00:00Z","timestamp":1774310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"The NNSF of China","award":["12271366, 12571391, 11871043"],"award-info":[{"award-number":["12271366, 12571391, 11871043"]}]},{"name":"The Science and Technology Innovation Plan of Shanghai,China","award":["23JC1403200"],"award-info":[{"award-number":["23JC1403200"]}]},{"name":"Singapore MOE AcRF Tier 1","award":["RG95\/23"],"award-info":[{"award-number":["RG95\/23"]}]},{"name":"Singapore MOE AcRF Tier 2","award":["MOE-T2EP20224-0012"],"award-info":[{"award-number":["MOE-T2EP20224-0012"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1007\/s10915-026-03252-5","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T06:52:10Z","timestamp":1774335130000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Error Analysis of Legendre Spectral Methods for the Monge-Amp\u00e8re Equation on Convex Quadrilaterals and Hexahedra"],"prefix":"10.1007","volume":"107","author":[{"given":"Lixiang","family":"Jin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3843-2143","authenticated-orcid":false,"given":"Zhaoxiang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-Lian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,24]]},"reference":[{"issue":"4","key":"3252_CR1","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1007\/s10444-014-9391-y","volume":"41","author":"G Awanou","year":"2015","unstructured":"Awanou, G.: Pseudo transient continuation and time marching methods for Monge-Amp\u00e8re type equations. Adv. Comput. Math. 41(4), 907\u2013935 (2015)","journal-title":"Adv. Comput. Math."},{"issue":"3","key":"3252_CR2","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1093\/imanum\/dru028","volume":"35","author":"G Awanou","year":"2015","unstructured":"Awanou, G.: Standard finite elements for the numerical resolution of the elliptic Monge-Amp\u00e8re equation: Classical solutions. IMA J. Numer. Anal. 35(3), 1150\u20131166 (2015)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"3252_CR3","doi-asserted-by":"publisher","first-page":"547","DOI":"10.4208\/jcm.1901-m2018-0039","volume":"38","author":"G Awanou","year":"2020","unstructured":"Awanou, G.: A two-grid method for the $$C^{0}$$ interior penalty discretization of the Monge-Amp\u00e8re equation. J. Comput. Math. 38(4), 547\u2013564 (2020)","journal-title":"J. Comput. Math."},{"key":"3252_CR4","doi-asserted-by":"crossref","unstructured":"Benamou, J.D., Froese, B.D., Oberman, A.M.: Two numerical methods for the elliptic Monge-Amp\u00e8re equation. ESAIM Math. Model. Numer. Anal. 44(4), 737\u2013758 (2010)","DOI":"10.1051\/m2an\/2010017"},{"key":"3252_CR5","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.enganabound.2020.12.007","volume":"124","author":"JJ Benito","year":"2021","unstructured":"Benito, J.J., Garc\u00eda, \u00c1., Gavete, L., Negreanu, M., Ure\u0148a, F., Vargas, A.M.: Solving Monge-Amp\u00e8re equation in 2D and 3D by generalized finite difference method. Eng. Anal. Boundary Elem. 124, 52\u201363 (2021)","journal-title":"Eng. Anal. Boundary Elem."},{"key":"3252_CR6","doi-asserted-by":"crossref","unstructured":"Bernardi, C., Maday, Y.: Spectral methods. In Handbook of Numerical Analysis, volume\u00a05 of Techniques of Scientific Computing (Part 2), pages 209\u2013485. Elsevier, January (1997)","DOI":"10.1016\/S1570-8659(97)80003-8"},{"issue":"3","key":"3252_CR7","doi-asserted-by":"publisher","first-page":"1212","DOI":"10.1137\/040621740","volume":"46","author":"K B\u00f6hmer","year":"2008","unstructured":"B\u00f6hmer, K.: On finite element methods for fully nonlinear elliptic equations of second order. SIAM J. Numer. Anal. 46(3), 1212\u20131249 (2008)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"3252_CR8","doi-asserted-by":"publisher","first-page":"1979","DOI":"10.1137\/23M1576839","volume":"62","author":"Y Boubendir","year":"2024","unstructured":"Boubendir, Y., Brusca, J., Hamfeldt, B.F., Takahashi, T.: Domain decomposition methods for the Monge-Amp\u00e8re equation. SIAM J. Numer. Anal. 62(4), 1979\u20132003 (2024)","journal-title":"SIAM J. Numer. Anal."},{"key":"3252_CR9","volume-title":"Chebyshev and Fourier Spectral Methods","author":"JP Boyd","year":"2001","unstructured":"Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Courier Corporation, Massachusetts (2001)"},{"issue":"276","key":"3252_CR10","doi-asserted-by":"publisher","first-page":"1979","DOI":"10.1090\/S0025-5718-2011-02487-7","volume":"80","author":"SC Brenner","year":"2011","unstructured":"Brenner, S.C., Gudi, T., Neilan, M., Sung, L.: $$C^0$$ penalty methods for the fully nonlinear Monge-Amp\u00e8re equation. Math. Comput. 80(276), 1979\u20131995 (2011)","journal-title":"Math. Comput."},{"key":"3252_CR11","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Neilan, M.: Finite element approximations of the three dimensional Monge-Amp\u00e8re equation. ESAIM Math. Model. Numer. Anal. 46(5), 979\u20131001 (2012)","DOI":"10.1051\/m2an\/2011067"},{"issue":"3","key":"3252_CR12","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s00211-021-01210-x","volume":"148","author":"SC Brenner","year":"2021","unstructured":"Brenner, S.C., Sung, L., Tan, Z., Zhang, H.: A convexity enforcing $$C^0$$ interior penalty method for the Monge-Amp\u00e8re equation on convex polygonal domains. Numer. Math. 148(3), 497\u2013524 (2021)","journal-title":"Numer. Math."},{"key":"3252_CR13","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Sung, L., Tan, Z., Zhang, H.: A nonlinear least-squares convexity enforcing $$C^0$$ interior penalty method for the Monge-Amp\u00e8re equation on strictly convex smooth planar domains. Commun. Am. Math. Soc. 4, 607\u2013640 (2024)","DOI":"10.1090\/cams\/39"},{"issue":"3","key":"3252_CR14","doi-asserted-by":"publisher","first-page":"A1097","DOI":"10.1137\/22M1494658","volume":"45","author":"J Brusca","year":"2023","unstructured":"Brusca, J., Hamfeldt, B.F.: A convergent quadrature-based method for the Monge-Amp\u00e8re equation. SIAM J. Sci. Comput. 45(3), A1097\u2013A1124 (2023)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"3252_CR15","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s10915-018-0698-6","volume":"77","author":"A Caboussat","year":"2018","unstructured":"Caboussat, A., Glowinski, R., Gourzoulidis, D.: A least-squares\/relaxation method for the numerical solution of the three-dimensional elliptic Monge-Amp\u00e8re equation. J. Sci. Comput. 77(1), 53\u201378 (2018)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"3252_CR16","doi-asserted-by":"publisher","first-page":"135","DOI":"10.2307\/1971510","volume":"131","author":"LA Caffarelli","year":"1990","unstructured":"Caffarelli, L.A.: Interior $$W^{2, p}$$ estimates for solutions of the Monge-Amp\u00e8re equation. Ann. Math. 131(1), 135\u2013150 (1990)","journal-title":"Ann. Math."},{"issue":"3","key":"3252_CR17","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1002\/cpa.3160370306","volume":"37","author":"LA Caffarelli","year":"1984","unstructured":"Caffarelli, L.A., Nirenberg, L., Spruck, J.: The dirichlet problem for nonlinear second-order elliptic equations I. Monge-Amp\u00e8re equation. Commun. Pure Appl. Math. 37(3), 369\u2013402 (1984)","journal-title":"Commun. Pure Appl. Math."},{"key":"3252_CR18","doi-asserted-by":"publisher","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, Germany (2006)"},{"issue":"2","key":"3252_CR19","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10444-021-09847-w","volume":"47","author":"H Chen","year":"2021","unstructured":"Chen, H., Feng, X., Zhang, Z.: A recovery-based linear $$C^0$$ finite element method for a fourth-order singularly perturbed Monge-Amp\u00e8re equation. Adv. Comput. Math. 47(2), 21 (2021)","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"3252_CR20","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1137\/110825960","volume":"55","author":"X Feng","year":"2013","unstructured":"Feng, X., Glowinski, R., Neilan, M.: Recent developments in numerical methods for fully nonlinear second order partial differential equations. SIAM Rev. 55(2), 205\u2013267 (2013)","journal-title":"SIAM Rev."},{"issue":"2","key":"3252_CR21","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1137\/070710378","volume":"47","author":"X Feng","year":"2009","unstructured":"Feng, X., Neilan, M.: Mixed finite element methods for the fully nonlinear Monge-Amp\u00e8re equation based on the vanishing moment method. SIAM J. Numer. Anal. 47(2), 1226\u20131250 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"3252_CR22","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10915-010-9439-1","volume":"47","author":"X Feng","year":"2011","unstructured":"Feng, X., Neilan, M.: Analysis of Galerkin methods for the fully nonlinear Monge-Amp\u00e8re equation. J. Sci. Comput. 47(3), 303\u2013327 (2011)","journal-title":"J. Sci. Comput."},{"key":"3252_CR23","doi-asserted-by":"publisher","DOI":"10.4171\/170","volume-title":"The Monge-Amp\u00e8re Equation and its Applications","author":"A Figalli","year":"2017","unstructured":"Figalli, A.: The Monge-Amp\u00e8re Equation and its Applications. European Mathematical Society Z\u00fcrich, Switzerland (2017)"},{"issue":"4","key":"3252_CR24","doi-asserted-by":"publisher","first-page":"1692","DOI":"10.1137\/100803092","volume":"49","author":"BD Froese","year":"2011","unstructured":"Froese, B.D., Oberman, A.M.: Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Amp\u00e8re equation in dimensions two and higher. SIAM J. Numer. Anal. 49(4), 1692\u20131714 (2011)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"3252_CR25","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1016\/j.jcp.2010.10.020","volume":"230","author":"BD Froese","year":"2011","unstructured":"Froese, B.D., Oberman, A.M.: Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\u00e8re equation. J. Comput. Phys. 230(3), 818\u2013834 (2011)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"3252_CR26","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1137\/120875065","volume":"51","author":"BD Froese","year":"2013","unstructured":"Froese, B.D., Oberman, A.M.: Convergent filtered schemes for the Monge-Amp\u00e8re partial differential equation. SIAM J. Numer. Anal. 51(1), 423\u2013444 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"342","key":"3252_CR27","doi-asserted-by":"publisher","first-page":"1467","DOI":"10.1090\/mcom\/3794","volume":"92","author":"D Gallistl","year":"2023","unstructured":"Gallistl, D., Tran, N.T.: Convergence of a regularized finite element discretization of the two-dimensional Monge-Amp\u00e8re equation. Math. Comput. 92(342), 1467\u20131490 (2023)","journal-title":"Math. Comput."},{"issue":"1","key":"3252_CR28","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s00211-023-01385-5","volume":"156","author":"D Gallistl","year":"2024","unstructured":"Gallistl, D., Tran, N.T.: Stability and guaranteed error control of approximations to the Monge-Amp\u00e8re equation. Numer. Math. 156(1), 107\u2013131 (2024)","journal-title":"Numer. Math."},{"key":"3252_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61798-0","volume-title":"Elliptic Partial Differential Equations of Second Order","author":"D Gilbarg","year":"2001","unstructured":"Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001). (Reprint of the 1998 edition)"},{"key":"3252_CR30","first-page":"71","volume":"22","author":"R Glowinski","year":"2006","unstructured":"Glowinski, R.: An augmented lagrangian approach to the numerical solution of the dirichlet problem for the elliptic Monge-Amp\u00e8re in two dimensions. Electron. Trans. Numer. Anal. 22, 71\u201396 (2006)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"1","key":"3252_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-018-0839-y","volume":"79","author":"R Glowinski","year":"2019","unstructured":"Glowinski, R., Liu, H., Leung, S., Qian, J.: A finite element\/operator-splitting method for the numerical solution of the two dimensional elliptic Monge-Amp\u00e8re equation. J. Sci. Comput. 79(1), 1\u201347 (2019)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3252_CR32","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/s10915-020-01226-9","volume":"83","author":"G Yiqi","year":"2020","unstructured":"Yiqi, G., Shen, J.: Accurate and efficient spectral methods for elliptic PDEs in complex domains. J. Sci. Comput. 83(3), 42 (2020)","journal-title":"J. Sci. Comput."},{"key":"3252_CR33","doi-asserted-by":"publisher","DOI":"10.1142\/3662","volume-title":"Spectral Methods and Their Applications","author":"B Guo","year":"1998","unstructured":"Guo, B.: Spectral Methods and Their Applications. World Scientific, Singapore; River Edge, N.J. (1998)"},{"issue":"5","key":"3252_CR34","doi-asserted-by":"publisher","first-page":"962","DOI":"10.1016\/j.cam.2011.04.027","volume":"236","author":"B Guo","year":"2011","unstructured":"Guo, B., Jia, H.: Pseudospectral method for quadrilaterals. J. Comput. Appl. Math. 236(5), 962\u2013979 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"3252_CR35","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s10444-005-7471-8","volume":"26","author":"B Guo","year":"2007","unstructured":"Guo, B., Wang, L.: Error analysis of spectral method on a triangle. Adv. Comput. Math. 26, 473\u2013496 (2007)","journal-title":"Adv. Comput. Math."},{"issue":"4","key":"3252_CR36","first-page":"664","volume":"12","author":"B Guo","year":"2015","unstructured":"Guo, B., Wang, T.: A spectral method for mixed boundary value problems on hexahedrons. Int. J. Numer. Anal. Model. 12(4), 664\u2013683 (2015)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"3252_CR37","doi-asserted-by":"crossref","unstructured":"Guti\u00e9rrez, C.E.: The Monge-Amp\u00e8re Equation, volume\u00a089 of Progress in Nonlinear Differential Equations and Their Applications. Springer International Publishing, Cham, (2016)","DOI":"10.1007\/978-3-319-43374-5"},{"key":"3252_CR38","doi-asserted-by":"crossref","unstructured":"Jia, H., Guo, B.: Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons. Chinese Ann. Math. Ser. B 31(6), 855\u2013878 (2010)","DOI":"10.1007\/s11401-010-0614-3"},{"key":"3252_CR39","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1016\/j.apnum.2024.09.028","volume":"207","author":"L Jin","year":"2025","unstructured":"Jin, L., Li, Z., Wang, P., Yi, L.: Spectral-Galerkin methods for the fully nonlinear Monge-Amp\u00e8re equation. Appl. Numer. Math. 207, 621\u2013641 (2025)","journal-title":"Appl. Numer. Math."},{"key":"3252_CR40","volume-title":"Spectral\/hp Element Methods for Computational Fluid Dynamics","author":"G Karniadakis","year":"2013","unstructured":"Karniadakis, G., Sherwin, S.: Spectral\/hp Element Methods for Computational Fluid Dynamics. Oxford University Press, USA (2013)"},{"issue":"2","key":"3252_CR41","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1007\/s10915-023-02183-9","volume":"95","author":"M Lai","year":"2023","unstructured":"Lai, M., Lee, J.: Trivariate spline collocation methods for numerical solution to 3D Monge-Amp\u00e8re equation. J. Sci. Comput. 95(2), 56 (2023)","journal-title":"J. Sci. Comput."},{"issue":"271","key":"3252_CR42","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1090\/S0025-5718-09-02308-4","volume":"79","author":"H Li","year":"2010","unstructured":"Li, H., Shen, J.: Optimal error estimates in Jacobi-weighted sobolev spaces for polynomial approximations on the triangle. Math. Comput. 79(271), 1621\u20131646 (2010)","journal-title":"Math. Comput."},{"issue":"5","key":"3252_CR43","doi-asserted-by":"publisher","first-page":"A3230","DOI":"10.1137\/23M1590779","volume":"46","author":"H Liu","year":"2024","unstructured":"Liu, H., Leung, S., Qian, J.: Operator-splitting\/finite element methods for the minkowski problem. SIAM J. Sci. Comput. 46(5), A3230\u2013A3257 (2024)","journal-title":"SIAM J. Sci. Comput."},{"key":"3252_CR44","first-page":"1","volume":"2020","author":"Z Liu","year":"2020","unstructured":"Liu, Z., Qiuyan, X.: On multiscale RBF collocation methods for solving the Monge-Amp\u00e8re equation. Math. Probl. Eng. 2020, 1\u201310 (2020)","journal-title":"Math. Probl. Eng."},{"issue":"3","key":"3252_CR45","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s00211-009-0283-x","volume":"115","author":"M Neilan","year":"2010","unstructured":"Neilan, M.: A nonconforming Morley finite element method for the fully nonlinear Monge-Amp\u00e8re equation. Numer. Math. 115(3), 371\u2013394 (2010)","journal-title":"Numer. Math."},{"key":"3252_CR46","first-page":"262","volume":"41","author":"M Neilan","year":"2014","unstructured":"Neilan, M.: A unified analysis of three finite element methods for the Monge-Amp\u00e8re equation. Electron. Trans. Numer. Anal. 41, 262\u2013288 (2014)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"316","key":"3252_CR47","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1090\/mcom\/3353","volume":"88","author":"RH Nochetto","year":"2019","unstructured":"Nochetto, R.H., Ntogkas, D., Zhang, W.: Two-scale method for the Monge-Amp\u00e8re equation: convergence to the viscosity solution. Math. Comput. 88(316), 637\u2013664 (2019)","journal-title":"Math. Comput."},{"issue":"3","key":"3252_CR48","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1093\/imanum\/dry026","volume":"39","author":"RH Nochetto","year":"2019","unstructured":"Nochetto, R.H., Ntogkas, D., Zhang, W.: Two-scale method for the Monge-Amp\u00e8re equation: pointwise error estimates. IMA J. Numer. Anal. 39(3), 1085\u20131109 (2019)","journal-title":"IMA J. Numer. Anal."},{"key":"3252_CR49","doi-asserted-by":"crossref","unstructured":"Oliker, V.I., Prussner, L.D.: On the numerical solution of the equation $$\\frac{{\\partial ^2 z}}{{\\partial x^2 }}\\frac{{\\partial ^2 z}}{{\\partial y^2 }} - \\left( {\\frac{{\\partial ^2 z}}{{\\partial x\\partial y}}} \\right)^2 = f$$ and its discretizations. I. Numer. Math. 54(3), 271\u2013293 (1989)","DOI":"10.1007\/BF01396762"},{"issue":"6","key":"3252_CR50","doi-asserted-by":"publisher","first-page":"A3728","DOI":"10.1137\/19M1245888","volume":"41","author":"S Olver","year":"2019","unstructured":"Olver, S., Townsend, A., Vasil, G.: A sparse spectral method on triangles. SIAM J. Sci. Comput. 41(6), A3728\u2013A3756 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"3252_CR51","doi-asserted-by":"crossref","unstructured":"Savin, O.: Global $$W^{2, p}$$ estimates for the Monge-Amp\u00e8re equation. Proc. Amer. Math. Soc.141(10), 3573\u20133578 (2013)","DOI":"10.1090\/S0002-9939-2013-11748-X"},{"key":"3252_CR52","volume-title":"Spectral and High-Order Methods with Applications","author":"J Shen","year":"2006","unstructured":"Shen, J., Tang, T.: Spectral and High-Order Methods with Applications. Science Press Beijing, China (2006)"},{"key":"3252_CR53","doi-asserted-by":"crossref","unstructured":"Shen, J., Tang, T., Wang, L.: Spectral Methods: Algorithms, Analysis and Applications. Number\u00a041 in Springer Series in Computational Mathematics. Springer, Heidelberg New York, (2011)","DOI":"10.1007\/978-3-540-71041-7"},{"issue":"2","key":"3252_CR54","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/s10915-024-02776-y","volume":"102","author":"C Wang","year":"2025","unstructured":"Wang, C., Wang, Z., Wang, Z.: A multi-domain spectral method with mapping techniques for the Fokker-Planck equation in irregular domains. J. Sci. Comput. 102(2), 52 (2025)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3252_CR55","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10915-024-02617-y","volume":"100","author":"P Wang","year":"2024","unstructured":"Wang, P., Jin, L., Li, Z., Yi, L.: Spectral collocation method for numerical solution to the fully nonlinear Monge-Amp\u00e8re equation. J. Sci. Comput. 100(3), 77 (2024)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3252_CR56","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1007\/s10915-015-0106-4","volume":"67","author":"T Wang","year":"2016","unstructured":"Wang, T.: A spectral method for fourth-order mixed inhomogeneous boundary value problem in three dimensions. J. Sci. Comput. 67(3), 1247\u20131271 (2016)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"3252_CR57","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10915-023-02207-4","volume":"95","author":"Z Wang","year":"2023","unstructured":"Wang, Z., Wen, X., Yao, G.: An efficient spectral-Galerkin method for elliptic equations in 2D complex geometries. J. Sci. Comput. 95(3), 89 (2023)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"3252_CR58","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s10915-015-0031-6","volume":"66","author":"Yu Xuhong","year":"2016","unstructured":"Xuhong, Yu., Guo, B.: Spectral method for fourth-order problems on quadrilaterals. J. Sci. Comput. 66(2), 477\u2013503 (2016)","journal-title":"J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03252-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-026-03252-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03252-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T16:02:43Z","timestamp":1778688163000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-026-03252-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,24]]},"references-count":58,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["3252"],"URL":"https:\/\/doi.org\/10.1007\/s10915-026-03252-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,24]]},"assertion":[{"value":"14 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"42"}}