{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T05:05:24Z","timestamp":1783573524723,"version":"3.55.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2017,2,4]],"date-time":"2017-02-04T00:00:00Z","timestamp":1486166400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11571290"],"award-info":[{"award-number":["11571290"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NSAF","award":["U1630247"],"award-info":[{"award-number":["U1630247"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s10444-017-9515-2","type":"journal-article","created":{"date-parts":[[2017,2,4]],"date-time":"2017-02-04T04:43:50Z","timestamp":1486183430000},"page":"1023-1058","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Dimension-by-dimension moment-based central Hermite WENO schemes for directly solving Hamilton-Jacobi equations"],"prefix":"10.1007","volume":"43","author":[{"given":"Zhanjing","family":"Tao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3479-0536","authenticated-orcid":false,"given":"Jianxian","family":"Qiu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,2,4]]},"reference":[{"key":"9515_CR1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1007633810484","volume":"15","author":"S Augoula","year":"2000","unstructured":"Augoula, S., Abgrall, R.: High order numerical discretization for Hamilton-Jacobi equations on triangular meshes. J. Sci. Comput. 15, 197\u2013229 (2000)","journal-title":"J. Sci. Comput."},{"key":"9515_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcph.1998.6007","volume":"145","author":"TJ Barth","year":"1998","unstructured":"Barth, T.J., Sethian, J.A.: Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains. J. Comput. Phys. 145, 1\u201340 (1998)","journal-title":"J. Comput. Phys."},{"key":"9515_CR3","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1137\/S1064827597324998","volume":"21","author":"F Bianco","year":"1999","unstructured":"Bianco, F., Puppo, G., Russo, G.: High-order central schemes for hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 21, 294\u2013322 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR4","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1137\/S1064827501394969","volume":"25","author":"S Bryson","year":"2003","unstructured":"Bryson, S., Levy, D.: Central schemes for multi-dimensional Hamilton-Jacobi equations. SIAM J. Sci. Comput. 25, 767\u2013791 (2003)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR5","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1137\/S0036142902408404","volume":"41","author":"S Bryson","year":"2003","unstructured":"Bryson, S., Levy, D.: High-order central WENO schemes for multidimensional Hamilton-Jacobi equations. SIAM J. Numer. Anal. 41, 1339\u20131369 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"9515_CR6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0021-9991(03)00201-8","volume":"189","author":"S Bryson","year":"2003","unstructured":"Bryson, S., Levy, D.: High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton-Jacobi equations. J. Comput. Phys. 189, 63\u201387 (2003)","journal-title":"J. Comput. Phys."},{"key":"9515_CR7","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.jcp.2006.09.012","volume":"223","author":"YD Cheng","year":"2007","unstructured":"Cheng, Y.D., Shu, C. -W.: A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations. J. Comput. Phys. 223, 398\u2013415 (2007)","journal-title":"J. Comput. Phys."},{"key":"9515_CR8","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jcp.2014.02.041","volume":"268","author":"YD Cheng","year":"2014","unstructured":"Cheng, Y.D., Wang, Z.: A new discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations. J. Comput. Phys. 268, 134\u2013153 (2014)","journal-title":"J. Comput. Phys."},{"key":"9515_CR9","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/S0002-9947-1984-0732102-X","volume":"282","author":"MG Crandall","year":"1984","unstructured":"Crandall, M.G., Evans, L.C., Lions, P.L.: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 282, 487\u2013502 (1984)","journal-title":"Trans. Am. Math. Soc."},{"key":"9515_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"MG Crandall","year":"1983","unstructured":"Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277, 1\u201342 (1983)","journal-title":"Trans. Am. Math. Soc."},{"key":"9515_CR11","doi-asserted-by":"crossref","first-page":"8209","DOI":"10.1016\/j.jcp.2008.05.025","volume":"227","author":"M Dumbser","year":"2008","unstructured":"Dumbser, M., Balsara, D.S., Toro, E.F., Munz, C. -D.: A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. J. Comput. Phys. 227, 8209\u20138253 (2008)","journal-title":"J. Comput. Phys."},{"key":"9515_CR12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0021-9991(87)90031-3","volume":"71","author":"A Harten","year":"1987","unstructured":"Harten, A., Engquist, B., Osher, S., Chakravathy, S.: Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71, 231\u2013303 (1987)","journal-title":"J. Comput. Phys."},{"key":"9515_CR13","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1137\/S1064827598337282","volume":"21","author":"C Hu","year":"1998","unstructured":"Hu, C., Shu, C.-W.: A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 666\u2013690 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR14","doi-asserted-by":"crossref","first-page":"2126","DOI":"10.1137\/S106482759732455X","volume":"21","author":"G Jiang","year":"1999","unstructured":"Jiang, G., Peng, D.: Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2126\u20132143 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR15","doi-asserted-by":"crossref","first-page":"2385","DOI":"10.1137\/S0036142996314366","volume":"35","author":"S Jin","year":"1998","unstructured":"Jin, S., Xin, Z.: Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and relaxation schemes. SIAM J. Numer. Anal. 35, 2385\u20132404 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"9515_CR16","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1006\/jcph.2000.6485","volume":"160","author":"A Kurganov","year":"2000","unstructured":"Kurganov, A., Tadmor, E.: New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations. J. Comput. Phys. 160, 720\u2013742 (2000)","journal-title":"J. Comput. Phys."},{"key":"9515_CR17","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jcph.1996.0021","volume":"123","author":"F Lafon","year":"1996","unstructured":"Lafon, F., Osher, S.: High order two-dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations. J. Comput. Phys. 123, 235\u2013253 (1996)","journal-title":"J. Comput. Phys."},{"key":"9515_CR18","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/cpa.3160130205","volume":"13","author":"PD Lax","year":"1960","unstructured":"Lax, P.D., Wendroff, B.: Systems of conservation laws. Commun. Pure Appl. Math. 13, 217\u2013237 (1960)","journal-title":"Commun. Pure Appl. Math."},{"key":"9515_CR19","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/S0168-9274(99)00109-9","volume":"33","author":"O Lepsky","year":"2000","unstructured":"Lepsky, O., Hu, C., Shu, C.-W.: Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations. Appl. Numer. Math. 33, 423\u2013434 (2000)","journal-title":"Appl. Numer. Math."},{"key":"9515_CR20","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1007\/s10915-009-9340-y","volume":"45","author":"F Li","year":"2010","unstructured":"Li, F., Yakovlev, S.: A central discontinuous Galerkin method for Hamilton-Jacobi equations. J. Sci. Comput. 45, 404\u2013428 (2010)","journal-title":"J. Sci. Comput."},{"key":"9515_CR21","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.cam.2003.09.051","volume":"167","author":"XG Li","year":"2004","unstructured":"Li, X.G., Chan, C.K.: High-order schemes for Hamilton-Jacobi equations on triangular meshes. J. Comput. Appl. Math. 167, 227\u2013241 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"9515_CR22","doi-asserted-by":"crossref","first-page":"2163","DOI":"10.1137\/S1064827598344856","volume":"21","author":"CT Lin","year":"2000","unstructured":"Lin, C.T., Tadmor, E.: High-resolution nonoscillatory central schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2163\u20132186 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR23","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/PL00005430","volume":"87","author":"CT Lin","year":"2001","unstructured":"Lin, C.T., Tadmor, E.: L\n                    1-stability and error estimates for approximate Hamilton-Jacobi solutions. Numer. Math. 87, 701\u2013735 (2001)","journal-title":"Numer. Math."},{"key":"9515_CR24","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jcp.2005.03.014","volume":"209","author":"Y Liu","year":"2005","unstructured":"Liu, Y.: Central schemes on overlapping cells. J. Comput. Phys. 209, 82\u2013104 (2005)","journal-title":"J. Comput. Phys."},{"key":"9515_CR25","doi-asserted-by":"crossref","first-page":"5489","DOI":"10.1016\/j.jcp.2012.05.011","volume":"231","author":"H Luo","year":"2012","unstructured":"Luo, H., Xia, Y., Li, S., Nourgaliev, R., Cai, C.: A Hermite WENO Reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids. J. Comput. Phys. 231, 5489\u20135503 (2012)","journal-title":"J. Comput. Phys."},{"key":"9515_CR26","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S Osher","year":"1988","unstructured":"Osher, S., Sethian, J.A.: Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"9515_CR27","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1137\/0728049","volume":"28","author":"S Osher","year":"1991","unstructured":"Osher, S., Shu, C.-W.: High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28, 907\u2013922 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"9515_CR28","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.cam.2006.01.022","volume":"200","author":"J Qiu","year":"2007","unstructured":"Qiu, J.: WENO Schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations. J. Comput. Appl. Math. 200, 591\u2013605 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"9515_CR29","first-page":"131","volume":"25","author":"J Qiu","year":"2007","unstructured":"Qiu, J.: Hermite WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations. J. Comput. Math. 25, 131\u2013144 (2007)","journal-title":"J. Comput. Math."},{"key":"9515_CR30","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jcp.2004.10.003","volume":"204","author":"J Qiu","year":"2005","unstructured":"Qiu, J., Shu, C.-W.: Hermite WENO schemes for Hamilton-Jacobi equations. J. Comput. Phys. 204, 82\u201399 (2005)","journal-title":"J. Comput. Phys."},{"key":"9515_CR31","volume-title":"High order numerical methods for time dependent Hamilton-Jacobi equations, Technical Report 11","author":"C-W Shu","year":"2007","unstructured":"Shu, C.-W.: High order numerical methods for time dependent Hamilton-Jacobi equations, Technical Report 11. Institute for Mathematical Sciences National University of Singapore, Mathematics and Computation in Imaging Science and Information Processing (2007)"},{"key":"9515_CR32","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jcp.2014.10.027","volume":"281","author":"Z Tao","year":"2015","unstructured":"Tao, Z., Li, F., Qiu, J.: High-order central Hermite WENO schemes on staggered meshes for hyperbolic conservation laws. J. Comput. Phys. 281, 148\u2013176 (2015)","journal-title":"J. Comput. Phys."},{"key":"9515_CR33","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.jcp.2016.05.005","volume":"318","author":"Z Tao","year":"2016","unstructured":"Tao, Z., Li, F., Qiu, J.: High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions. J. Comput. Phys. 318, 222\u2013251 (2016)","journal-title":"J. Comput. Phys."},{"key":"9515_CR34","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.jcp.2010.09.022","volume":"230","author":"J Yan","year":"2011","unstructured":"Yan, J., Osher, S.: A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations. J. Comput. Phys. 230, 232\u2013244 (2011)","journal-title":"J. Comput. Phys."},{"key":"9515_CR35","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1090\/S0025-5718-1986-0815835-1","volume":"46","author":"M Zennaro","year":"1986","unstructured":"Zennaro, M.: Natural continuous extensions of Runge-Kutta methods. Math. Comput. 46, 119\u2013133 (1986)","journal-title":"Math. Comput."},{"key":"9515_CR36","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1137\/S1064827501396798","volume":"24","author":"YT Zhang","year":"2003","unstructured":"Zhang, Y.T., Shu, C.-W.: High order WENO schemes for Hamilton-Jacobi equations on triangular meshes. SIAM J. Sci. Comput. 24, 1005\u20131030 (2003)","journal-title":"SIAM J. Sci. Comput."},{"key":"9515_CR37","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.jcp.2015.12.011","volume":"307","author":"F Zheng","year":"2016","unstructured":"Zheng, F., Qiu, J.: Directly solving the Hamilton-Jacobi equations by Hermite WENO schemes. J. Comput. Phys. 307, 423\u2013445 (2016)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-017-9515-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-017-9515-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-017-9515-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,11,6]],"date-time":"2017-11-06T06:04:47Z","timestamp":1509948287000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-017-9515-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,4]]},"references-count":37,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["9515"],"URL":"https:\/\/doi.org\/10.1007\/s10444-017-9515-2","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,4]]}}}