{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T12:34:18Z","timestamp":1762864458756},"reference-count":29,"publisher":"Elsevier BV","issue":"36","license":[{"start":{"date-parts":[[2002,8,1]],"date-time":"2002-08-01T00:00:00Z","timestamp":1028160000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computer Methods in Applied Mechanics and Engineering"],"published-print":{"date-parts":[[2002,8]]},"DOI":"10.1016\/s0045-7825(02)00334-1","type":"journal-article","created":{"date-parts":[[2002,10,11]],"date-time":"2002-10-11T11:30:57Z","timestamp":1034335857000},"page":"3909-3928","source":"Crossref","is-referenced-by-count":32,"title":["Adaptive multiresolution approach for solution of hyperbolic PDEs"],"prefix":"10.1016","volume":"191","author":[{"given":"M.A.","family":"Alves","sequence":"first","affiliation":[]},{"given":"P.","family":"Cruz","sequence":"additional","affiliation":[]},{"given":"A.","family":"Mendes","sequence":"additional","affiliation":[]},{"given":"F.D.","family":"Magalh\u00e3es","sequence":"additional","affiliation":[]},{"given":"F.T.","family":"Pinho","sequence":"additional","affiliation":[]},{"given":"P.J.","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0045-7825(02)00334-1_BIB1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1080\/00411459608220705","article-title":"Adaptive wavelet collocation method for the solution of Burgers equation","volume":"25","author":"Bertoluzza","year":"1996","journal-title":"Transp. Theory Statist. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB2","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1137\/S106482759426955X","article-title":"Design and application of a gradient-weighted moving finite element code I: In one dimension","volume":"19","author":"Carlson","year":"1998","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB3","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/cpa.3160050303","article-title":"The solution of nonlinear hyperbolic differential equations by finite differences","volume":"5","author":"Courant","year":"1952","journal-title":"Commun. Pure Appl. Math."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB4","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/10407799608915080","article-title":"Normalized variable and space formulation methodology for high-resolution schemes","volume":"30","author":"Darwish","year":"1994","journal-title":"Numer. Heat Transfer Part B"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB5","series-title":"Computational Methods for Fluid Dynamics","author":"Ferziger","year":"1996"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB6","series-title":"Computational Techniques for Fluid Dynamics, vol. I","author":"Fletcher","year":"1991"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB7","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1115\/1.2910144","article-title":"Policy statement on the control of numerical accuracy","volume":"115","author":"Freitas","year":"1993","journal-title":"ASME J. Fluids Engrg."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB8","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/fld.1650080602","article-title":"Curvature compensated convective transport: SMART, a new boundedness preserving transport algorithm","volume":"8","author":"Gaskell","year":"1988","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB9","first-page":"271","article-title":"A difference scheme for numerical computations of discontinuous solution of hydrodynamic equations","volume":"47","author":"Godunov","year":"1959","journal-title":"Math. Sbornik"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB10","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0021-9991(83)90136-5","article-title":"High resolution schemes for hyperbolic conservation laws","volume":"49","author":"Harten","year":"1983","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB11","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0021-9991(87)90031-3","article-title":"Uniformly high order accurate essentially non-oscillatory schemes","volume":"71","author":"Harten","year":"1987","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB12","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1137\/0733060","article-title":"Multiresolution representation of data: A general framework","volume":"33","author":"Harten","year":"1996","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB13","series-title":"Numerical Computation of Internal and External Flows, vol. 2","author":"Hirsch","year":"1990"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB14","first-page":"405","article-title":"Solving hyperbolic PDEs using interpolating wavelets","volume":"21","author":"Holmstr\u00f6m","year":"1999","journal-title":"J. Sci. Comput."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB15","unstructured":"L. Jameson, Wavelet-based grid generation, ICASE Report No. 96-59, NASA Langley Research Center, Hampton, 1996"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB16","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1093\/imanum\/19.4.609","article-title":"An unconditionally stable splitting scheme for a class of nonlinear parabolic equations","volume":"19","author":"Karlsen","year":"1999","journal-title":"IMA J. Numer. Anal."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB17","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1006\/jcph.2000.6459","article-title":"New high-resolution central schemes for nonlinear conservation laws and convection\u2013diffusion equations","volume":"160","author":"Kurganov","year":"2000","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB18","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1002\/cpa.3160070112","article-title":"Weak solutions of nonlinear hyperbolic equations and their numerical computation","volume":"7","author":"Lax","year":"1954","journal-title":"Commun. Pure Appl. Math."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB19","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0045-7825(79)90034-3","article-title":"A stable and accurate convective modeling procedure based on quadratic upstream interpolation","volume":"19","author":"Leonard","year":"1979","journal-title":"Comput. Meth. Appl. Mech. Engrg."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB20","first-page":"35","article-title":"Locally modified QUICK scheme for highly convective 2-D and 3-D flows","volume":"vol. 5","author":"Leonard","year":"1987"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB21","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1002\/fld.1650081013","article-title":"Simple high-accuracy resolution program for convective modelling of discontinuities","volume":"8","author":"Leonard","year":"1988","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB22","first-page":"69","article-title":"Multiresolution approximation and wavelet orthogonal bases of L2(R)","volume":"315","author":"Mallat","year":"1989","journal-title":"Trans. Am. Math. Soc."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB23","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1137\/0904010","article-title":"Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations","volume":"4","author":"Petzold","year":"1983","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB24","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/0021-9991(85)90188-3","article-title":"A study of finite difference approximations to steady-state convection dominated flow problems","volume":"57","author":"Shyy","year":"1985","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(78)90023-2","article-title":"A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws","volume":"22","author":"Sod","year":"1978","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB26","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1002\/(SICI)1097-0363(20000415)32:7<881::AID-FLD2>3.0.CO;2-6","article-title":"On a higher-order bounded discretization scheme","volume":"32","author":"Song","year":"2000","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"10.1016\/S0045-7825(02)00334-1_BIB27","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1137\/0721062","article-title":"High resolution schemes using flux limiters for hyperbolic conservation laws","volume":"21","author":"Sweby","year":"1984","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB28","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1137\/S0036142996313130","article-title":"Filter bank methods for hyperbolic PDEs","volume":"36","author":"Wald\u00e9n","year":"1999","journal-title":"J. Numer. Anal."},{"key":"10.1016\/S0045-7825(02)00334-1_BIB29","unstructured":"H.-M. Zhou, Wavelet transforms and PDE techniques in image compression, Ph.D. Thesis, Department of Mathematics, UCLA, 2000"}],"container-title":["Computer Methods in Applied Mechanics and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0045782502003341?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0045782502003341?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T09:27:52Z","timestamp":1554974872000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0045782502003341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,8]]},"references-count":29,"journal-issue":{"issue":"36","published-print":{"date-parts":[[2002,8]]}},"alternative-id":["S0045782502003341"],"URL":"https:\/\/doi.org\/10.1016\/s0045-7825(02)00334-1","relation":{},"ISSN":["0045-7825"],"issn-type":[{"value":"0045-7825","type":"print"}],"subject":[],"published":{"date-parts":[[2002,8]]}}}