{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T19:42:52Z","timestamp":1793130172630,"version":"4.5.0"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>This paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives: the renormalized meshfree derivatives, which improve the consistency of the original weighted particle methods. The weak renormalized meshfree scheme, built from the weak formulation of general conservation laws, turns out to be $L^2$ stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field. A time discretization is then performed by analogy with finite volume methods, and the $L^1$, $L^\\infty$, and $BV$ stabilities of the obtained time discretized scheme are studied. From the same analogy with finite volume methods, a hybrid particle scheme is built using the Godunov method and is numerically compared to the weak renormalized scheme.<\/jats:p>","DOI":"10.1137\/s0036142903427718","type":"journal-article","created":{"date-parts":[[2008,4,18]],"date-time":"2008-04-18T18:06:43Z","timestamp":1208542003000},"page":"1912-1934","source":"Crossref","is-referenced-by-count":70,"title":["Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws"],"prefix":"10.1137","volume":"46","author":[{"given":"Nathalie","family":"Lanson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Paul","family":"Vila","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,18]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0732036"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"B. Ben Moussa, N. Lanson, and J. P. Vila,\n                      Convergence of meshless methods for conservation laws: Applications to Euler equations\n                      , in Hyperbolic Problems: Theory, Numerics, Applications, Vol. I (Z\u00fcrich, $1998$), Internat. Ser. Numer. Math. 129, Birkh\u00e4user, Basel, 1999, pp. 31\u201340.","DOI":"10.1007\/978-3-0348-8720-5_4"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996307119"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0912064"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90036-0"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90066-9"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19960830)39:16<2725::AID-NME973>3.0.CO;2-9"},{"key":"R8","unstructured":"N. Lanson,\n                      Etude des m\u00e9thodes particulaires renormalis\u00e9es. Applications aux prob\u00e8mes de dynamique rapide.\n                      , Ph.D. thesis, INSA-Universit\u00e9 Paul Sabatier, Toulouse, France, 2001, www.math.uwaterloo.ca\/~nlanson\/thesis1.pdf."},{"key":"R9","first-page":"465","volume":"340","author":"Lanson N.","year":"2005","journal-title":"Les Comptes Rendus de l'Acad\u00e9mie des Sciences"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290444739X"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.aa.30.090192.002551"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0721016"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"R. W. Randles and L. D. Libertsky,\n                      Smoothed particle hydrodynamics: Some recent improvements and applications\n                      , Comput. Methods Appl. Mech. Engrg., 139 (1996) pp. 375\u2013408.","DOI":"10.1016\/S0045-7825(96)01090-0"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"P. A. Raviart,\n                      An analysis of particle methods\n                      , in Numerical Methods in Fluid Dynamics (Como, 1983), F. Brezzi, ed., Lecture Notes in Math. 1127, Springer-Verlag, Berlin, 1985, pp. 243\u2013324.","DOI":"10.1007\/BFb0074532"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1984-0758189-X"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(79)90145-1"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202599000117"},{"key":"R18","unstructured":"J. P. Vila,\n                      Weighted particle-finite volume hybrid schemes\n                      , in Finite Volumes for Complex Applications, F. Benkhaldoun and R. Vilsmeier, eds., Hermes, Paris, 1996."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036142903427718","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:10Z","timestamp":1787325250000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036142903427718"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/S0036142903427718"],"URL":"https:\/\/doi.org\/10.1137\/s0036142903427718","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}