{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:16:54Z","timestamp":1776838614370,"version":"3.51.2"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,10,17]],"date-time":"2009-10-17T00:00:00Z","timestamp":1255737600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s00211-009-0271-1","type":"journal-article","created":{"date-parts":[[2009,10,16]],"date-time":"2009-10-16T10:33:36Z","timestamp":1255689216000},"page":"1-44","source":"Crossref","is-referenced-by-count":12,"title":["Convergence of a non-monotone scheme for Hamilton\u2013Jacobi\u2013Bellman equations with discontinous initial data"],"prefix":"10.1007","volume":"115","author":[{"given":"Olivier","family":"Bokanowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nadia","family":"Megdich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hasnaa","family":"Zidani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,10,17]]},"reference":[{"issue":"2","key":"271_CR1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1007633810484","volume":"15","author":"R. Agbrall","year":"2000","unstructured":"Agbrall R., Augoula S.: High order numerical discretization for Hamilton-Jacobi equations on triangular meshes. J. Sci. Comput. 15(2), 197\u2013229 (2000)","journal-title":"J. Sci. Comput."},{"key":"271_CR2","doi-asserted-by":"crossref","unstructured":"Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. In: Systems and Control: Foundations and Applications. Birkh\u00e4user, Boston (1997)","DOI":"10.1007\/978-0-8176-4755-1"},{"key":"271_CR3","volume-title":"Solutions de viscosit\u00e9 des \u00e9quations de Hamilton-Jacobi, volume 17 of Math\u00e9matiques & Applications (Berlin)","author":"G. Barles","year":"1994","unstructured":"Barles G.: Solutions de viscosit\u00e9 des \u00e9quations de Hamilton-Jacobi, volume 17 of Math\u00e9matiques & Applications (Berlin). Springer-Verlag, Paris (1994)"},{"key":"271_CR4","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3233\/ASY-1991-4305","volume":"4","author":"G. Barles","year":"1991","unstructured":"Barles G., Souganidis P.E.: Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4, 271\u2013283 (1991)","journal-title":"Asymptot. Anal."},{"key":"271_CR5","doi-asserted-by":"crossref","unstructured":"Bokanowski, O., Forcadel, N., Zidani, H.: L 1-error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1. Math. Comput. (to appear) (2009)","DOI":"10.1090\/S0025-5718-10-02311-2"},{"issue":"9","key":"271_CR6","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/j.apnum.2006.03.004","volume":"56","author":"O. Bokanowski","year":"2006","unstructured":"Bokanowski O., Martin S., Munos R., Zidani H.: An anti-diffusive scheme for viability problems. Appl. Numer. Math. 56(9), 1135\u20131254 (2006)","journal-title":"Appl. Numer. Math."},{"key":"271_CR7","first-page":"256","volume":"5","author":"O. Bokanowski","year":"2006","unstructured":"Bokanowski O., Megdich N., Zidani H.: An adaptative antidissipative method for optimal control problems. Arima 5, 256\u2013271 (2006)","journal-title":"Arima"},{"issue":"1","key":"271_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-005-9017-0","volume":"30","author":"O. Bokanowski","year":"2007","unstructured":"Bokanowski O., Zidani H.: Anti-diffusive schemes for linear advection and application to Hamilton-Jacobi-Bellman equations. J. Sci. Comput. 30(1), 1\u201333 (2007)","journal-title":"J. Sci. Comput."},{"issue":"218","key":"271_CR9","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1090\/S0025-5718-97-00838-7","volume":"66","author":"B. Cockburn","year":"1997","unstructured":"Cockburn B., Gremaud P.-A.: A priori error estimates for numerical methods for scalar conservation laws. II. Flux-splitting monotone schemes on irregular Cartesian grids. Math. Comput. 66(218), 547\u2013572 (1997)","journal-title":"Math. Comput."},{"key":"271_CR10","doi-asserted-by":"crossref","unstructured":"Cockburn, B., Gremaud, P.-A., Yang, J.X.: A priori error estimates for numerical methods for scalar conservation laws. III. Multidimensional flux-splitting monotone schemes on non-Cartesian grids. SIAM J. Numer. Anal. 35(5), 1775\u20131803 (electronic) (1998)","DOI":"10.1137\/S0036142997316165"},{"key":"271_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0025-5718-1984-0744921-8","volume":"43","author":"M.G. Crandall","year":"1984","unstructured":"Crandall M.G., Lions P.-L.: Two approximations of solutions of Hamilton Jacobi equations. Math. Comput. 43, 1\u201319 (1984)","journal-title":"Math. Comput."},{"key":"271_CR12","doi-asserted-by":"crossref","unstructured":"Despr\u00e8s, B.: Lax theorem and finite volume schemes. Math. Comput. 73(247), 1203\u20131234 (electronic) (2004)","DOI":"10.1090\/S0025-5718-03-01618-1"},{"key":"271_CR13","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1023\/A:1013298408777","volume":"16","author":"B. Despr\u00e8s","year":"2001","unstructured":"Despr\u00e8s B., Lagouti\u00e8re F.: Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. J. Sci. Comput. 16, 479\u2013524 (2001)","journal-title":"J. Sci. Comput."},{"key":"271_CR14","unstructured":"Falcone, M.: A numerical approach to the infinite horizon problem. Appl. Math. Optim. 15(13), 213\u2013214 (1987), and 23 (1991)"},{"key":"271_CR15","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1006\/jcph.2001.6954","volume":"175","author":"M. Falcone","year":"2002","unstructured":"Falcone M., Ferretti R.: Semi-lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods. J. Comput. Phys. 175, 559\u2013575 (2002)","journal-title":"J. Comput. Phys."},{"key":"271_CR16","unstructured":"Godlewski, E., Raviart, P.-A.: Hyperbolic Systems of Conservation Laws. SMAI. Ellipses (1991)"},{"issue":"7","key":"271_CR17","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.crma.2004.01.024","volume":"338","author":"F. Lagoutiere","year":"2004","unstructured":"Lagoutiere F.: A non-dissipative entropic scheme for convex scalar equations via discontinuous cell reconstruction. C. R. Acad. Sci. 338(7), 549\u2013554 (2004)","journal-title":"C. R. Acad. Sci."},{"key":"271_CR18","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s002110050102","volume":"69","author":"P.L. Lions","year":"1995","unstructured":"Lions P.L., Souganidis P.E.: Convergence of muscle and filtered schemes for scalar conservation laws and Hamilton Jacobi equations. Numer. Math. 69, 441\u2013470 (1995)","journal-title":"Numer. Math."},{"issue":"4","key":"271_CR19","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 essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28(4), 907\u2013922 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"271_CR20","volume-title":"Real and Complex Analysis","author":"W. Rudin","year":"1987","unstructured":"Rudin W.: Real and Complex Analysis, 3rd edn. McGraw-Hill Book Co., New York (1987)","edition":"3"},{"key":"271_CR21","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01204182","volume":"29","author":"P. Saint-Pierre","year":"1994","unstructured":"Saint-Pierre P.: Approximation of viability kernel. Appl. Math. Optim. 29, 187\u2013209 (1994)","journal-title":"Appl. Math. Optim."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-009-0271-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-009-0271-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-009-0271-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,23]],"date-time":"2020-05-23T02:55:19Z","timestamp":1590202519000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-009-0271-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,17]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["271"],"URL":"https:\/\/doi.org\/10.1007\/s00211-009-0271-1","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10,17]]}}}