{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T10:51:54Z","timestamp":1763808714894},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,11,27]],"date-time":"2007-11-27T00:00:00Z","timestamp":1196121600000},"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":[[2008,1]]},"DOI":"10.1007\/s00211-007-0120-z","type":"journal-article","created":{"date-parts":[[2007,11,26]],"date-time":"2007-11-26T11:37:33Z","timestamp":1196077053000},"page":"407-444","source":"Crossref","is-referenced-by-count":12,"title":["Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system"],"prefix":"10.1007","volume":"108","author":[{"given":"Martin","family":"Campos Pinto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Mehrenberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,11,27]]},"reference":[{"issue":"1","key":"120_CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0041-5553(75)90141-X","volume":"15","author":"A. Arsen\u2019ev","year":"1975","unstructured":"Arsen\u2019ev, A.: Global existence of a weak solution of Vlasov\u2019s system of equations. U.S.S.R. Comput. Math. Math. Phys. 15(1), 131\u2013143 (1975)","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"issue":"2","key":"120_CR2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/S0294-1449(16)30405-X","volume":"2","author":"C. Bardos","year":"1985","unstructured":"Bardos, C., Degond, P.: Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 2(2), 101\u2013118 (1985)","journal-title":"Ann. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire"},{"issue":"3","key":"120_CR3","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/0022-0396(77)90049-3","volume":"25","author":"J. Batt","year":"1977","unstructured":"Batt, J.: Global symmetric solutions of the initial value problem of stellar dynamics. J. Differ. Equ. 25(3), 342\u2013364 (1977)","journal-title":"J. Differ. Equ."},{"issue":"1","key":"120_CR4","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/0021-9991(89)90035-1","volume":"82","author":"M. Berger","year":"1989","unstructured":"Berger, M., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82(1), 64\u201384 (1989)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"120_CR5","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/0021-9991(84)90073-1","volume":"53","author":"M. Berger","year":"1984","unstructured":"Berger, M., Oliger, J.: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53(3), 484\u2013512 (1984)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"120_CR6","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1137\/S0036142902410775","volume":"42","author":"N. Besse","year":"2004","unstructured":"Besse, N.: Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system. SIAM J. Numer. Anal. 42(1), 350\u2013382 (2004) (electronic)","journal-title":"SIAM J. Numer. Anal."},{"key":"120_CR7","first-page":"437","volume-title":"Numerical Mathematics and Advanced Applications ENUMATH 2001","author":"N. Besse","year":"2001","unstructured":"Besse, N., Filbet, F., Gutnic, M., Paun, I., Sonnendr\u00fccker, E.: An adaptive numerical method for the Vlasov equation based on a multiresolution analysis. In: Brezzi, F., Buffa, A., Escorsaro, S., Murli, A.(eds) Numerical Mathematics and Advanced Applications ENUMATH 2001, pp. 437\u2013446. Springer, Heidelberg (2001)"},{"key":"120_CR8","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1090\/S0025-5718-07-01912-6","volume":"77","author":"N. Besse","year":"2008","unstructured":"Besse, N., Mehrenberger, M.: Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system. Math. Comput. 77, 93\u2013123 (2008)","journal-title":"Math. Comput."},{"issue":"2","key":"120_CR9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/S0021-9991(03)00318-8","volume":"191","author":"N. Besse","year":"2003","unstructured":"Besse, N., Sonnendr\u00fccker, E.: Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. J. Comput. Phys. 191(2), 341\u2013376 (2003)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"120_CR10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s00211-003-0492-7","volume":"97","author":"P. Binev","year":"2004","unstructured":"Binev, P., Dahmen, W., DeVore, R.: Adaptive finite element methods with convergence rates. Numer. Math. 97(2), 219\u2013268 (2004)","journal-title":"Numer. Math."},{"key":"120_CR11","volume-title":"Plasma Physics via Computer Simulation","author":"C.K. Birdsall","year":"1985","unstructured":"Birdsall, C.K., Langdon, A.B.: Plasma Physics via Computer Simulation. McGraw-Hill, New York (1985)"},{"key":"120_CR12","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1017\/S0962492904000182","volume":"13","author":"H.-J. Bungartz","year":"2004","unstructured":"Bungartz, H.-J., Griebel, M.: Sparse grids. Acta Numer. 13, 147\u2013269 (2004)","journal-title":"Acta Numer."},{"key":"120_CR13","unstructured":"Campos Pinto, M.: D\u00e9veloppement et analyse de sch\u00e9mas adaptatifs pour les \u00e9quations de transport. U. P. et M. Curie, Paris, 2005. PhD Thesis (in french)"},{"key":"120_CR14","unstructured":"Campos Pinto, M.: A total curvature diminishing property for P 1 finite element interpolation. Math. Forschungs. Oberwolfach Report, 34\/2004, 2005"},{"key":"120_CR15","doi-asserted-by":"crossref","unstructured":"Campos Pinto, M., Mehrenberger, M.: Adaptive numerical resolution of the Vlasov equation. Numerical methods for hyperbolic and kinetic problems, CEMRACS 2003\/IRMA Lectures in Math. and Theoretical Physics, 2005","DOI":"10.4171\/012-1\/3"},{"key":"120_CR16","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/0021-9991(76)90053-X","volume":"22","author":"C.Z. Cheng","year":"1976","unstructured":"Cheng, C.Z., Knorr, G.: The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330\u2013351 (1976)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"120_CR17","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1137\/S1064827599363988","volume":"23","author":"G. Chiavassa","year":"2001","unstructured":"Chiavassa, G., Donat, R.: Point value multiscale algorithms for 2D compressible flows. SIAM J. Sci. Comput. 23(3), 805\u2013823 (2001) (electronic)","journal-title":"SIAM J. Sci. Comput."},{"key":"120_CR18","doi-asserted-by":"crossref","unstructured":"Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Handbook of Numerical Analysis, vol. II, pp. 17\u2013351. North-Holland, Amsterdam (1991)","DOI":"10.1016\/S1570-8659(05)80039-0"},{"key":"120_CR19","unstructured":"Cohen, A.: Numerical analysis of wavelet methods, volume 32 of Studies in Mathematics and its Applications. North-Holland, Amsterdam (2003)"},{"issue":"241","key":"120_CR20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1090\/S0025-5718-01-01391-6","volume":"72","author":"A. Cohen","year":"2003","unstructured":"Cohen, A., Kaber, S.M., M\u00fcller, S., Postel, M.: Fully adaptive multiresolution finite volume schemes for conservation laws. Math. Comput. 72(241), 183\u2013225 (2003) (electronic)","journal-title":"Math. Comput."},{"issue":"2","key":"120_CR21","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/0022-247X(80)90082-7","volume":"75","author":"J. Cooper","year":"1980","unstructured":"Cooper, J., Klimas, A.: Boundary value problems for the Vlasov-Maxwell equation in one dimension. J. Math. Anal. Appl. 75(2), 306\u2013329 (1980)","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"120_CR22","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0021-9045(82)90060-0","volume":"36","author":"W. Dahmen","year":"1982","unstructured":"Dahmen, W.: Adaptive approximation by multivariate smooth splines. J. Approx. Theory 36(2), 119\u2013140 (1982)","journal-title":"J. Approx. Theory"},{"key":"120_CR23","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1017\/S0962492900002713","volume":"6","author":"W. Dahmen","year":"1997","unstructured":"Dahmen, W.: Wavelet and multiscale methods for operator equations. Acta Numer. 6, 55\u2013228 (1997)","journal-title":"Acta Numer."},{"issue":"3","key":"120_CR24","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s211-001-8009-3","volume":"88","author":"W. Dahmen","year":"2001","unstructured":"Dahmen, W., Gottschlich-M\u00fcller, B., M\u00fcller, S.: Multiresolution schemes for conservation laws. Numer. Math. 88(3), 399\u2013443 (2001)","journal-title":"Numer. Math."},{"issue":"3","key":"120_CR25","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1137\/S106482759935544X","volume":"23","author":"W. Dahmen","year":"2001","unstructured":"Dahmen, W., M\u00fcller, S., Schlinkmann, T.: On an adaptive multigrid solver for convection-dominated problems. SIAM J. Sci. Comput. 23(3), 781\u2013804 (2001) (electronic)","journal-title":"SIAM J. Sci. Comput."},{"key":"120_CR26","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1017\/S0962492900002816","volume":"7","author":"R. DeVore","year":"1998","unstructured":"DeVore, R.: Nonlinear approximation. Acta Numer. 7, 51\u2013150 (1998)","journal-title":"Acta Numer."},{"key":"120_CR27","unstructured":"Filbet, F., Sonnendr\u00fccker, E.: Numerical methods for the Vlasov equation. In: Brezzi, F., Buffa, A., Escorsaro, S., Murli, A. (eds.) Numerical Mathematics and Advanced Applications ENUMATH 2001. Springer, Heidelberg, 2001"},{"issue":"3","key":"120_CR28","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0010-4655(02)00694-X","volume":"150","author":"F. Filbet","year":"2003","unstructured":"Filbet, F., Sonnendr\u00fccker, E.: Comparison of Eulerian Vlasov solvers. Comput. Phys. Comm. 150(3), 247\u2013266 (2003)","journal-title":"Comput. Phys. Comm."},{"key":"120_CR29","doi-asserted-by":"crossref","unstructured":"Glassey, R.T.: The Cauchy problem in kinetic theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1996)","DOI":"10.1137\/1.9781611971477"},{"key":"120_CR30","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF02123478","volume":"4","author":"M. Griebel","year":"1999","unstructured":"Griebel, M., Oswald, P.: Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems. Adv. Comput. Math 4, 171\u2013206 (1999)","journal-title":"Adv. Comput. Math"},{"key":"120_CR31","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.cpc.2004.06.073","volume":"164","author":"M. Gutnic","year":"2004","unstructured":"Gutnic, M., Haefele, M., Paun, I., Sonnendr\u00fccker, E.: Vlasov simulations on an adaptive phase-space grid. Comput. Phys. Commun. 164, 214\u2013219 (2004)","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"120_CR32","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1006\/jcph.1994.1199","volume":"115","author":"A. Harten","year":"1994","unstructured":"Harten, A.: Adaptive multiresolution schemes for shock computations. J. Comput. Phys. 115(2), 319\u2013338 (1994)","journal-title":"J. Comput. Phys."},{"issue":"12","key":"120_CR33","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1002\/cpa.3160481201","volume":"48","author":"A. Harten","year":"1995","unstructured":"Harten, A.: Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. Commun. Pure Appl. Math. 48(12), 1305\u20131342 (1995)","journal-title":"Commun. Pure Appl. Math."},{"issue":"2","key":"120_CR34","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/mma.1670030117","volume":"3","author":"E. Horst","year":"1981","unstructured":"Horst, E.: On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation I. General theory. Math. Methods Appl. Sci. 3(2), 229\u2013248 (1981)","journal-title":"General theory. Math. Methods Appl. Sci."},{"issue":"1","key":"120_CR35","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/mma.1670040104","volume":"4","author":"E. Horst","year":"1982","unstructured":"Horst, E.: On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation II. Special cases. Math. Methods Appl. Sci. 4(1), 19\u201332 (1982)","journal-title":"Math. Methods Appl. Sci."},{"issue":"233","key":"120_CR36","first-page":"77","volume":"70","author":"P. Houston","year":"2001","unstructured":"Houston, P., S\u00fcli, E.: Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems. Technical Report NA-95\/24, Oxford University Computing Lab., 1995. Published in Math. Comp. 70(233), 77\u2013106 (2001)","journal-title":"Technical Report NA-95\/24, Oxford University Computing Lab., 1995. Published in Math. Comp."},{"issue":"35","key":"120_CR37","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1090\/trans2\/035\/12","volume":"2","author":"S.V. Iordanskii","year":"1964","unstructured":"Iordanskii, S.V.: The Cauchy problem for the kinetic equation of plasma. Am. Math. Soc. Transl. Ser. 2(35), 351\u2013363 (1964)","journal-title":"Am. Math. Soc. Transl. Ser."},{"issue":"2","key":"120_CR38","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/BF01232273","volume":"105","author":"P.-L. Lions","year":"1991","unstructured":"Lions, P.-L., Perthame, B.: Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105(2), 415\u2013430 (1991)","journal-title":"Invent. Math."},{"key":"120_CR39","unstructured":"Ne\u010das, J.: Les m\u00e9thodes directes en th\u00e9orie des \u00e9quations elliptiques. Masson et Cie, \u00c9diteurs, Paris (1967)"},{"key":"120_CR40","doi-asserted-by":"crossref","unstructured":"Rault, A., Chiavassa, G., Donat, R.: Shock-vortex interactions at high Mach numbers. J. Sci. Comput. 19(1-3), 347\u2013371 (2003) Special issue in honor of the sixtieth birthday of Stanley Osher","DOI":"10.1023\/A:1025316311633"},{"key":"120_CR41","unstructured":"Raviart, P.-A.: An analysis of particle methods. In: Numerical methods in fluid dynamics (Como, 1983), volume 1127 of Lecture Notes in Math., pp. 243\u2013324. Springer, Berlin, 1985"},{"issue":"2","key":"120_CR42","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/S0021-9991(03)00189-X","volume":"188","author":"O. Roussel","year":"2003","unstructured":"Roussel, O., Schneider, K., Tsigulin, A., Bockhorn, H.: A conservative fully adaptive multiresolution algorithm for parabolic PDEs. J. Comput. Phys. 188(2), 493\u2013523 (2003)","journal-title":"J. Comput. Phys."},{"issue":"8\u20139","key":"120_CR43","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1080\/03605309108820801","volume":"16","author":"J. Schaeffer","year":"1991","unstructured":"Schaeffer, J.: Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Commun. Partial Differ. Equ. 16(8\u20139), 1313\u20131335 (1991)","journal-title":"Commun. Partial Differ. Equ."},{"key":"120_CR44","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.cpc.2004.06.077","volume":"164","author":"E. Sonnendr\u00fccker","year":"2004","unstructured":"Sonnendr\u00fccker, E., Filbet, F., Friedman, A., Oudet, E., Vay, J.L.: Vlasov simulation of beams with a moving grid. Comput. Phys. Commun. 164, 390\u2013395 (2004)","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"120_CR45","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1006\/jcph.1998.6148","volume":"149","author":"E. Sonnendr\u00fccker","year":"1999","unstructured":"Sonnendr\u00fccker, E., Roche, J., Bertrand, P., Ghizzo, A.: The semi-Lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys. 149(2), 201\u2013220 (1999)","journal-title":"J. Comput. Phys."},{"key":"120_CR46","unstructured":"Yserentant, H.: Hierarchical bases. In: ICIAM 91 (Washington, DC, 1991), pp. 256\u2013276. SIAM, Philadelphia (1992)"},{"key":"120_CR47","unstructured":"Zenger, C.: Sparse grids. In Parallel algorithms for partial differential equations (Kiel, 1990), volume 31 of Notes Numer. Fluid Mech., pp. 241\u2013251. Vieweg, Braunschweig (1991)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0120-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0120-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0120-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T22:50:23Z","timestamp":1684104623000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0120-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,27]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["120"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0120-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,27]]}}}