{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:59Z","timestamp":1787337299628,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We derive closed form expressions for the eigenvalues and discrete solution arising from a 19\u2010point compact discretization of a three\u2010dimensional convection\u2010diffusion problem. It is shown that the coefficient matrix is positive definite when the cell\u2010Reynolds number is greater than some critical value. By analyzing the terms composing the discrete solution, we prove that an oscillation\u2010free discrete solution is guaranteed whenever the cell\u2010Reynolds number exceeds a value which is grid\u2010size dependent. An interesting result is that as the mesh size is refined, this value approaches the Golden Mean.<\/jats:p>","DOI":"10.1137\/s1064827502410797","type":"journal-article","created":{"date-parts":[[2006,12,11]],"date-time":"2006-12-11T14:43:47Z","timestamp":1165848227000},"page":"2075-2094","source":"Crossref","is-referenced-by-count":20,"title":["Analysis of a Fourth\u2010Order Scheme for a Three\u2010Dimensional Convection\u2010Diffusion Model Problem"],"prefix":"10.1137","volume":"28","author":[{"given":"Ashvin","family":"Gopaul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muddun","family":"Bhuruth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,12,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901374877"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-01-01392-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1002\/num.1041"},{"key":"R4","unstructured":"C. Greif,\n                      Analysis of Cyclic Reduction for the Numerical Solution of Three\u2010Dimensional Convection\u2010Diffusion Equations\n                      , Ph.D. thesis, The University of British Columbia, Vancouver, BC, Canada, 1998."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(99)00085-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5627"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/num.1690080606"},{"key":"R8","first-page":"211","volume":"6","author":"Pardhanani A. L.","year":"1997","journal-title":"Electron. Trans. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1097-4067","issn-type":"print"},{"key":"R9","unstructured":"A. Ramage,\n                      A Note on Parameter Choice and Iterative Convergence for Stabilised Discretisations of Advection\u2010Diffusion Problems in Three Dimensions\n                      , Technical report, Mathematics Research Report 32\/98, University of Strathclyde, Glasgow, Scotland, 1998."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1108\/09615539810206357"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5659"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-0887(199803)14:3<209::AID-CNM139>3.0.CO;2-P"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827502410797","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:30Z","timestamp":1787334930000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827502410797"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":12,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/S1064827502410797"],"URL":"https:\/\/doi.org\/10.1137\/s1064827502410797","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}