{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T07:57:36Z","timestamp":1761292656312},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,10,6]],"date-time":"2009-10-06T00:00:00Z","timestamp":1254787200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2010,7]]},"DOI":"10.1007\/s11075-009-9337-5","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T16:53:48Z","timestamp":1254761628000},"page":"325-342","source":"Crossref","is-referenced-by-count":7,"title":["Relaxation Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations"],"prefix":"10.1007","volume":"54","author":[{"given":"Peng","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuzi","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,10,6]]},"reference":[{"key":"9337_CR1","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1002\/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.0.CO;2-B","volume":"49","author":"R Abgrall","year":"1996","unstructured":"Abgrall, R.: Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes. Commun. Pure Appl. Math. 49, 1339\u20131373 (1996)","journal-title":"Commun. Pure Appl. Math."},{"key":"9337_CR2","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":"9337_CR3","first-page":"67","volume-title":"Collected Lectures on the Preservation of Stability Under Discretization","author":"B Cockburn","year":"2002","unstructured":"Cockburn, B., Qian, J.: Continuuos dependence results for Hamilton-Jacobi equations. In: Estep, D., Tavener, S. (eds.) Collected Lectures on the Preservation of Stability Under Discretization, pp. 67\u201390. SIAM, Philadelphia (2002)"},{"key":"9337_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"M Crandall","year":"1983","unstructured":"Crandall, M., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am.\u00a0Math. Soc. 277, 1\u201342 (1983)","journal-title":"Trans. Am.\u00a0Math. Soc."},{"key":"9337_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1984-0744921-8","volume":"43","author":"M Crandall","year":"1984","unstructured":"Crandall, M., Lions, P.L.: Two approximations of solutions of Hamilton-Jacobi equations. Math. Comput. 43, 1\u201319 (1984)","journal-title":"Math. Comput."},{"key":"9337_CR6","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1190\/1.1443639","volume":"59","author":"S Gray","year":"1994","unstructured":"Gray, S., May, W.: Kirchhoff migration using eikonal equation travel-times. Geophysics 59, 810\u2013817 (1994)","journal-title":"Geophysics"},{"key":"9337_CR7","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1137\/S1064827598337282","volume":"20","author":"C Hu","year":"1999","unstructured":"Hu, C., Shu, C.-W.: A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 20, 666\u2013690 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9337_CR8","doi-asserted-by":"crossref","first-page":"2126","DOI":"10.1137\/S106482759732455X","volume":"21","author":"G-S Jiang","year":"2000","unstructured":"Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2126\u20132143 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"9337_CR9","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jcp.2003.11.007","volume":"196","author":"CY Kao","year":"2004","unstructured":"Kao, C.Y., Osher, S., Qian, J.: Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations. J. Comput. Phys. 196, 367\u2013391 (2004)","journal-title":"J. Comput. Phys."},{"key":"9337_CR10","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1190\/1.1444693","volume":"64","author":"S Kim","year":"1999","unstructured":"Kim, S., Cook, R.: 3D traveltime computation using second-order ENO scheme. Geophysics 64, 1867\u20131876 (1999)","journal-title":"Geophysics"},{"key":"9337_CR11","doi-asserted-by":"crossref","first-page":"2229","DOI":"10.1137\/040612002","volume":"28","author":"D Levy","year":"2006","unstructured":"Levy, D., Nayak, S., Shu, C.-W., Zhang, Y.T.: Central WENO schemes for Hamilton-Jacobi equations on triangular meshes. SIAM J. Sci. Comput. 28, 2229\u20132247 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9337_CR12","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":"9337_CR13","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1137\/0524066","volume":"24","author":"S Osher","year":"1993","unstructured":"Osher, S.: A level set formulation for the solution of the Dirichlet problems for Hamilton-Jacobi equations. SIAM J. Math. Anal. 24, 1145\u20131152 (1993)","journal-title":"SIAM J. Math. Anal."},{"key":"9337_CR14","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1006\/jcph.2001.6875","volume":"174","author":"J Qian","year":"2001","unstructured":"Qian, J., Symes, W.W.: Paraxial eikonal solvers for anisotropic quasi-P travel times. J. Comput. Phys. 174, 256\u2013278 (2001)","journal-title":"J. Comput. Phys."},{"key":"9337_CR15","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1137\/050627083","volume":"45","author":"J Qian","year":"2007","unstructured":"Qian, J., Zhang, Y.-T., Zhao, H.-K.: Fast sweeping methods for Eikonal equations on triangular meshes. SIAM J. Numer. Anal. 45, 83\u2013107 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"9337_CR16","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s10915-006-9124-6","volume":"31","author":"J Qian","year":"2007","unstructured":"Qian, J., Zhang, Y.-T., Zhao, H.-K.: A fast sweeping method for static convex Hamilton-Jacobi equations. J. Sci. Comput. 31, 237\u2013271 (2007)","journal-title":"J. Sci. Comput."},{"key":"9337_CR17","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"JA Sethian","year":"1996","unstructured":"Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591\u20131595 (1996)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9337_CR18","doi-asserted-by":"crossref","unstructured":"Shu, C.-W.: High Order Numerical Methods for Time Dependent Hamilton-Jacobi Equations. WSPC\/Lecture Notes Series (2007)","DOI":"10.1142\/9789812709066_0002"},{"key":"9337_CR19","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"JN Tsitsiklis","year":"1995","unstructured":"Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Automat. Contr. 40, 1528\u20131538 (1995)","journal-title":"IEEE Trans. Automat. Contr."},{"key":"9337_CR20","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1137\/S1064827501396798","volume":"24","author":"Y-T 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":"9337_CR21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10915-005-9014-3","volume":"29","author":"Y-T Zhang","year":"2006","unstructured":"Zhang, Y.-T., Zhao, H.-K., Qian, J.: High order fast sweeping methods for static Hamilton-Jacobi equations. J. Sci. Comput. 29, 25\u201326 (2006)","journal-title":"J. Sci. Comput."},{"key":"9337_CR22","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1039\/D0AY02022B","volume":"13","author":"Y-T Zhang","year":"2006","unstructured":"Zhang, Y.-T., Zhao, H.-K., Chen, S.: Fixed-point iterative sweeping methods for static Hamilton-Jacobi equations. Methods Appl. Anal. 13, 299\u2013320 (2006)","journal-title":"Methods Appl. Anal."},{"key":"9337_CR23","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1090\/S0025-5718-04-01678-3","volume":"74","author":"H-K Zhao","year":"2005","unstructured":"Zhao, H.-K.: A fast sweeping method for eikonal equations. Math. Comput. 74, 603\u2013627 (2005)","journal-title":"Math. Comput."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9337-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-009-9337-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9337-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T20:59:35Z","timestamp":1633985975000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-009-9337-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,6]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,7]]}},"alternative-id":["9337"],"URL":"https:\/\/doi.org\/10.1007\/s11075-009-9337-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10,6]]}}}