{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T19:46:50Z","timestamp":1762112810500,"version":"3.44.0"},"reference-count":27,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Chemical Engineering Science"],"published-print":{"date-parts":[[2003,5]]},"DOI":"10.1016\/s0009-2509(03)00015-0","type":"journal-article","created":{"date-parts":[[2003,4,23]],"date-time":"2003-04-23T15:56:24Z","timestamp":1051113384000},"page":"1777-1792","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":18,"title":["Solution of hyperbolic PDEs using a stable adaptive multiresolution method"],"prefix":"10.1016","volume":"58","author":[{"given":"P.","family":"Cruz","sequence":"first","affiliation":[]},{"given":"M.A.","family":"Alves","sequence":"additional","affiliation":[]},{"given":"F.D.","family":"Magalh\u00e3es","sequence":"additional","affiliation":[]},{"given":"A.","family":"Mendes","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0009-2509(03)00015-0_BIB1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0377-0257(00)00198-1","article-title":"The flow of viscoelastic fluids past a cylinder","volume":"97","author":"Alves","year":"2001","journal-title":"Journal of Non-Newtonian Fluid Mechanics"},{"key":"10.1016\/S0009-2509(03)00015-0_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","volume":"19","author":"Carlson","year":"1998","journal-title":"SIAM Journal of Scientific Computing"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB3","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S1385-8947(00)00266-7","article-title":"Applications of a moving finite element method","volume":"84","author":"Coimbra","year":"2001","journal-title":"Chemical Engineering Journal"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB4","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":"Communications on Pure and Applied Mathematics"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB5","doi-asserted-by":"crossref","first-page":"3305","DOI":"10.1016\/S0009-2509(00)00551-0","article-title":"Using wavelets for solving PDEs","volume":"56","author":"Cruz","year":"2001","journal-title":"Chemical Engineering Science"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB6","first-page":"122","article-title":"Using in-bed temperature profiles for visualizing the concentration front movement","volume":"35","author":"Cruz","year":"2001","journal-title":"Chemical Engineering Education"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB7","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1002\/aic.690480412","article-title":"A wavelet-based adaptive grid for the solution of non-linear PDEs","volume":"48","author":"Cruz","year":"2002","journal-title":"A.I.Ch.E. Journal"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB8","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/10407799408914918","article-title":"Normalized variable and space formulation methodology for high-resolution schemes","volume":"26","author":"Darwish","year":"1994","journal-title":"Numerical Heat Transfer Part B-Fundamentals"},{"year":"1992","series-title":"Numerical methods for problems with moving fronts","author":"Finlayson","key":"10.1016\/S0009-2509(03)00015-0_BIB9"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB10","doi-asserted-by":"crossref","unstructured":"Fletcher, C. A. J. (1991). Computational techniques for fluid dynamics, Vol. I (2nd ed.). Berlin: Springer.","DOI":"10.1007\/978-3-642-58239-4"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB11","first-page":"339","article-title":"Policy statement on the control of numerical accuracy","volume":"115","author":"Freitas","year":"1993","journal-title":"ASME Journal of Fluids Engineering"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB12","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/fld.1650080602","article-title":"Curvature compensated convective transport","volume":"8","author":"Gaskell","year":"1988","journal-title":"International Journal for Numerical Methods in Fluids"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB13","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":"Journal of Computational Physics"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB14","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1137\/0733060","article-title":"Multiresolution representation of data","volume":"33","author":"Harten","year":"1996","journal-title":"SIAM Journal of Numerical Analysis"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB15","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1137\/S1064827597316278","article-title":"Solving hyperbolic PDEs using interpolation wavelets","volume":"21","author":"Holmstr\u00f6m","year":"1999","journal-title":"SIAM Journal of Scientific Computing"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB16","doi-asserted-by":"crossref","first-page":"1980","DOI":"10.1137\/S1064827596301534","article-title":"A wavelet-optimized, very high order adaptive order adaptive grid and order numerical method","volume":"19","author":"Jameson","year":"1998","journal-title":"SIAM Journal of Scientific Computing"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB17","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1006\/jcph.2000.6459","article-title":"New high-resolution central schemes for non-linear conservation laws and convection\u2013diffusion equations","volume":"160","author":"Kurganov","year":"2000","journal-title":"Journal of Compuational Physics"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB18","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0045-7825(79)90034-3","article-title":"A stable and accurate convective modelling procedure based on quadratic upstream interpolation","volume":"19","author":"Leonard","year":"1979","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB19","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":"International Journal of Numerical Methods in Fluids"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0045-7825(91)90232-U","article-title":"The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection","volume":"88","author":"Leonard","year":"1991","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB21","doi-asserted-by":"crossref","first-page":"1729","DOI":"10.1016\/S0009-2509(99)00462-5","article-title":"The wavelet-collocation method for transient problems with steep gradients","volume":"55","author":"Liu","year":"2000","journal-title":"Chemical Engineering Science"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB22","first-page":"69","article-title":"Multiresolution approximation and wavelet orthogonal bases of L2(R)","volume":"315","author":"Mallat","year":"1989","journal-title":"Transactions of the American Mathematical Society"},{"key":"10.1016\/S0009-2509(03)00015-0_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 Journal of Science and Statistical Computing"},{"year":"1995","series-title":"Applied mathematics and modeling for chemical engineers","author":"Rice","key":"10.1016\/S0009-2509(03)00015-0_BIB24"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB25","unstructured":"Roe, P. L. (1985). Large scale computations in fluid mechanics, Pt. 2. In E. Engquist, S. Osher, & R. J. C. Sommerville (Eds.), Lectures in Applied Mechanics, Vol. 22 (pp.163\u2013193). Providence, RI: American Mathematical Society."},{"year":"1994","series-title":"Pressure swing adsorption","author":"Ruthven","key":"10.1016\/S0009-2509(03)00015-0_BIB26"},{"key":"10.1016\/S0009-2509(03)00015-0_BIB27","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":"Journal of Computational Physics"}],"container-title":["Chemical Engineering Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0009250903000150?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0009250903000150?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,14]],"date-time":"2025-09-14T00:43:21Z","timestamp":1757810601000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0009250903000150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":27,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2003,5]]}},"alternative-id":["S0009250903000150"],"URL":"https:\/\/doi.org\/10.1016\/s0009-2509(03)00015-0","relation":{},"ISSN":["0009-2509"],"issn-type":[{"type":"print","value":"0009-2509"}],"subject":[],"published":{"date-parts":[[2003,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Solution of hyperbolic PDEs using a stable adaptive multiresolution method","name":"articletitle","label":"Article Title"},{"value":"Chemical Engineering Science","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0009-2509(03)00015-0","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Science Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}