{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:31:04Z","timestamp":1787383864395,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>\n                    A novel, comprehensive, discrete, half-space analysis for the defect-correction method has been developed. This analysis plays the same role for nonelliptic-problem solvers as the full-space Fourier mode analysis plays for elliptic-problem solvers. Numerical simulations confirm the accuracy of the half-space analysis. The following important findings about the defect-correction method applied to the Fromm discretization of the two-dimensional convection equation are reported: The initial convergence rate of the defect-correction method is principally a function of the relative accuracy of the operators involved in the defect-correction iterations. The asymptotic convergence rate is about 0.5 per defect-correction iteration.If the driver operator is first-order accurate, then the initial convergence rates may be slow. The number of iterations required to get into the asymptotic convergence regime or\/and to converge the algebraic error below the discretization-error level can be proportional to h\n                    <jats:sup>-1\/3<\/jats:sup>\n                    . This h-dependent delay is a multidimensional phenomenon---it cannot be observedin one-dimensional problems, and it disappears in the case of close alignment between the grid and the convection equation characteristic.If the driver operator is second-order accurate, the defect-correction solver demonstrates the asymptotic convergence rate from the very beginning. Only one defect-correction iteration is required to converge algebraic error substantially below the discretization-error level.\n                  <\/jats:p>","DOI":"10.1137\/s1064827599358637","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"633-655","source":"Crossref","is-referenced-by-count":10,"title":["Half-Space Analysis of the Defect-Correction Method for Fromm Discretization of Convection"],"prefix":"10.1137","volume":"22","author":[{"given":"Boris","family":"Diskin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James L.","family":"Thomas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"S. A. Allmaras,\n                      Multigrid for the 2\u2010D Compressible Navier\u2010Stokes Equations\n                      , AIAA Paper 99\u20103336, 14th AIAA CFD Conference, Norfolk, VA, 1999.","DOI":"10.2514\/6.1999-3336"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"K. B\u00f6hmer, P. Hemker, H. Stetter, The defect correction approach, Comput. Suppl., Vol. 5, Springer, Vienna, 1984, 1\u20133286i:65007","DOI":"10.1007\/978-3-7091-7023-6_1"},{"key":"R3","unstructured":"A. Brandt,\n                      Multigrid Solvers for Non\u2010Elliptic and Singular\u2010Perturbation Steady\u2010State Problems\n                      , manuscript, The Weizmann Institute of Science, Rehovot, Israel, 1981."},{"key":"R4","unstructured":"A. Brandt,\n                      The Weizmann Institute of Science research in multilevel computations: 1988 Report\n                      , inProceedings of the Fourth Copper Mountain Conference on Multigrid Methods, J. Mandel, S. F. McCormick, J. E. Dendy, Jr., C. Farhat, G. Lonsdale, S. V. Parker, J. W. Ruge, and K. Stuben, eds., SIAM, Philadelphia, 1989, pp. 13\u201353."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7930(98)00043-7"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90049-5"},{"key":"R7","unstructured":"J. A. D\u00e9sid\u00e9ri and P. W. Hemker,\n                      Analysis of Convergence of Iterative Implicit and Defect\u2010Correction Algorithms for Hyperbolic Problems\n                      , Report 1200, Institut National de Recherche en Informatique et en Automatique, Valbonne, France, 1990."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0916007"},{"key":"R9","unstructured":"B. Diskin,\n                      Solving Upwind\u2010Biased Discretizations II: Multigrid Solver Using Semicoarsening\n                      , ICASE Report 99\u201025, ICASE, Hampton, VA, 1999."},{"key":"R10","unstructured":"B. Diskin and J. L. Thomas,\n                      Solving Upwind\u2010Biased Discretizations: Defect\u2010Correction Iterations\n                      , ICASE Report 99\u201014, ICASE, Hampton, VA, 1999."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90162-3"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90223-N"},{"key":"R13","unstructured":"S. L. Krist, R. T. Biedron, and C. L. Rumsey,\n                      CFL3D User\u2019s Manual (Version 42 5.0)\n                      , NASA TM\u20101998\u2010208444, NASA, Hampton, VA, 1998."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5854"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"J. L. Thomas, D. L. Bonhaus, W. K. Anderson, C. L. Rumsey, and R. T. Biedron,\n                      An O(n,m2) Plane Solver for the Compressible Navier\u2010Stokes Equations\n                      , AIAA Paper 99\u20100785, 37th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1999.","DOI":"10.2514\/6.1999-785"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"J. L. Thomas, B. Diskin, and A. Brandt,\n                      Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier\u2010Stokes Equations\n                      , AIAA Paper 99\u20103334, 14th Computational Fluid Dynamics Conference, Norfolk, VA, 1999.","DOI":"10.2514\/6.1999-3334"},{"key":"R17","unstructured":"J. L. Thomas, B. Diskin, and A. Brandt,\n                      Textbook Multigrid Efficiency for the Incompressible Navier\u2010Stokes Equations: High Reynolds Number Wakes and Boundary Layers\n                      , ICASE Report 99\u201051, ICASE, Hampton, VA, 1999."},{"key":"R18","volume-title":"An introduction to multigrid methods","author":"Wesseling Pieter","year":"1992"},{"key":"R19","first-page":"776","volume":"182","author":"Yanenko N.","year":"1968","journal-title":"Dokl. Akad. Nauk SSSR","ISSN":"https:\/\/id.crossref.org\/issn\/0002-3264","issn-type":"print"},{"key":"R20","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1007\/BF00971662","volume":"10","author":"Yanenko N.","year":"1969","journal-title":"Siberian Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0037-4466","issn-type":"print"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599358637","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:40:00Z","timestamp":1787334000000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599358637"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599358637"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599358637","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}