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time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media","{\"openalex\":\"W2523474032\",\"doi\":\"10.1051/m2an/1983170302491\"}","2026-05-23T02:47:52.258018697","2026-05-23T02:47:52.258020877","doi","10.1051/m2an/1983170302491","arxivId","openalexId","W2523474032","abstractText","utilisation (http://","publishedDate","1983-01-01","publishedYear",1983,"venue","RAIRO Analyse numérique",228,"authors","keywords",[181,182,183],"pdfUrl","https://www.esaim-m2an.org/10.1051/m2an/1983170302491/pdf","topVenue","Advanced Numerical Methods in Computational Mathematics","Advanced Mathematical Modeling in Engineering","Numerical methods in engineering","paper_W2079318234","A family of higher order mixed finite element methods for plane elasticity","{\"openalex\":\"W2079318234\",\"doi\":\"10.1007/bf01379659\"}","2026-05-22T18:55:38.196309977","2026-05-22T18:55:38.196311609","10.1007/bf01379659","W2079318234","1984-02-01",1984,"Numerische Mathematik",238,[181,183,196],"Contact Mechanics and Variational Inequalities","paper_W2034150466","Stabilized mixed methods for the Stokes problem","{\"openalex\":\"W2034150466\",\"doi\":\"10.1007/bf01395886\"}","2026-05-22T06:06:07.190084837","2026-05-22T06:06:07.190086756","10.1007/bf01395886","W2034150466","1988-01-01",1988,259,[181,208,182],"Computational Fluid Dynamics and Aerodynamics","paper_W2065330829","On the Numerical Integration of $\\frac{\\partial ^2 u}{\\partial x^2 } + \\frac{\\partial ^2 u}{\\partial y^2 } = \\frac{\\partial u}{\\partial t}$ by Implicit Methods","{\"openalex\":\"W2065330829\",\"doi\":\"10.1137/0103004\"}","2026-05-21T14:49:46.259880578","2026-05-21T14:49:46.260366571","10.1137/0103004","W2065330829","Previous article On the Numerical Integration of $\\frac{\\partial ^2 u}{\\partial x^2 } + \\frac{\\partial ^2 u}{\\partial y^2 } = \\frac{\\partial u}{\\partial t}$ by Implicit MethodsJim Douglas, Jr.Jim Douglas, Jr.https://doi.org/10.1137/0103004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. H. Bruce, , D. W. Peaceman, , H. H. Rachford and , J. D. Rice, Calculations of unsteady-state gas flow through porous media, Journal of Petroleum technology, 198 (1953), 79–91 CrossrefGoogle Scholar[2] H. Lewy, , R. Courant and , K. Friedrichs, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann., 100 (1928), 32–74 10.1007/BF01448839 MR1512478 CrossrefGoogle Scholar[3] J. Crank and , P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Cambridge Philos. Soc., 43 (1947), 50–67 MR0019410 CrossrefISIGoogle Scholar[4] S. Hartree and , J. R. Womersley, A method for the numerical or mechanical solution of certain types of partial differential equations, Proc. Royal Soc. London, Series A, 161 (1937), 353–366 0017.08003 CrossrefGoogle Scholar[5] F. B. Hildebrand, On the convergence of numerical solutions of the heat-flow equation, J. Math. Physics, 31 (1952), 35–41 MR0048171 0048.07602 CrossrefISIGoogle Scholar[6] Fritz John, On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval, Comm. Pure Appl. Math., 5 (1952), 155–211 MR0047885 0047.33703 CrossrefISIGoogle Scholar[7] M. L. Juncosa and , D. M. Young, On the order of convergence of solutions of a difference equation to a solution of the diffusion equation, J. Soc. Indust. Appl. Math., 1 (1953), 111–135 10.1137/0101007 MR0060907 0053.46303 LinkGoogle Scholar[8] Pentti Laasonen, Über eine Methode zur Lösung der Wärmeleitungsgleichung, Acta Math., 81 (1949), 309–317 MR0032094 0040.35802 CrossrefISIGoogle Scholar[9] Werner Leutert, On the convergence of approximate solutions of the heat equation to the exact solution, Proc. Amer. Math. Soc., 2 (1951), 433–439 MR0043577 0043.12602 CrossrefISIGoogle Scholar[10] George G. O'Brien, , Morton A. Hyman and , Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics, 29 (1951), 223–251 MR0040805 0042.13204 CrossrefISIGoogle Scholar[11] D. W. Peaceman and , H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), 28–41 10.1137/0103003 MR0071874 0067.35801 LinkISIGoogle Scholar[12] Erich Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Math. Ann., 102 (1930), 650–670 10.1007/BF01782368 MR1512599 CrossrefGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails Method of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion for Phase-Field ModelsMatthew Causley, Hana Cho, and Andrew Christlieb12 October 2017 | SIAM Journal on Scientific Computing, Vol. 39, No. 5AbstractPDF (2175 KB)Method of Lines Transpose: High Order L-Stable ${\\mathcal O}(N)$ Schemes for Parabolic Equations Using Successive Convolution2 June 2016 | SIAM Journal on Numerical Analysis, Vol. 54, No. 3AbstractPDF (1298 KB)Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations12 June 2014 | SIAM Journal on Numerical Analysis, Vol. 52, No. 3AbstractPDF (453 KB)An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media29 January 2013 | SIAM Journal on Scientific Computing, Vol. 35, No. 1AbstractPDF (1869 KB)Difference Graphs of Block ADI Method26 July 2006 | SIAM Journal on Numerical Analysis, Vol. 38, No. 3AbstractPDF (162 KB)Domain Decomposition Operator Splittings for the Solution of Parabolic Equations25 July 2006 | SIAM Journal on Scientific Computing, Vol. 19, No. 3AbstractPDF (406 KB)Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative16 May 2012 | SIAM Journal on Scientific and Statistical Computing, Vol. 1, No. 1AbstractPDF (2857 KB)Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 3AbstractPDF (2718 KB)Rounding Errors in Alternating Direction Methods for Parabolic Problems3 August 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 2AbstractPDF (1267 KB)Alternating Direction Schemes for the Heat Equation in a General Domain14 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 3AbstractPDF (1121 KB)On Incomplete Iteration for Implicit Parabolic Difference Equations10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 3AbstractPDF (466 KB)An Alternating-Direction-Implicit Iteration Technique10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2AbstractPDF (1508 KB)On the Relation Between Stability and Convergence in the Numerical Solution of Linear Parabolic and Hyperbolic Differential Equations10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 4, No. 1AbstractPDF (1316 KB)The Numerical Solution of Parabolic and Elliptic Differential EquationsD. W. Peaceman and H. H. Rachford, Jr.10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 3, No. 1AbstractPDF (1199 KB) Volume 3, Issue 1| 1955Journal of the Society for Industrial and Applied Mathematics History Submitted:18 October 1954Published online:10 July 2006 InformationCopyright © 1955 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0103004Article page range:pp. 42-65ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics","1955-03-01",1955,"Journal of the Society for Industrial and Applied Mathematics",285,[181,182,222],"Numerical methods in inverse problems","paper_W2464997744","Efficient rectangular mixed finite elements in two and three space variables","{\"openalex\":\"W2464997744\",\"doi\":\"10.1051/m2an/1987210405811\"}","2026-05-20T13:18:47.257624055","2026-05-20T13:18:47.262522604","10.1051/m2an/1987210405811","W2464997744","avec les conditions gnrales d'utilisation (","1987-01-01",1987,"ESAIM Mathematical Modelling and Numerical Analysis",331,[181,183,182],"https://www.esaim-m2an.org/10.1051/m2an/1987210405811/pdf","paper_W1992358193","PEERS: A new mixed finite element for plane elasticity","{\"openalex\":\"W1992358193\",\"doi\":\"10.1007/bf03167064\"}","2026-05-20T01:54:49.238962542","2026-05-20T01:54:49.242286731","10.1007/bf03167064","W1992358193","1984-12-01","Japan Journal of Applied Mathematics",362,[248,181,196],"Elasticity and Material Modeling","paper_W204624611","The approximation of the pressure by a mixed method in the simulation of miscible displacement","{\"openalex\":\"W204624611\",\"doi\":\"10.1051/m2an/1983170100171\"}","2026-05-20T01:56:28.193970732","2026-05-20T01:56:28.194163521","10.1051/m2an/1983170100171","W204624611","utilisation (http://www.",[181,259,182],"https://www.esaim-m2an.org/10.1051/m2an/1983170100171/pdf","Enhanced Oil Recovery Techniques","paper_W2061172735","Global estimates for mixed methods for second order elliptic equations","{\"openalex\":\"W2061172735\",\"doi\":\"10.1090/s0025-5718-1985-0771029-9\"}","2026-05-16T08:28:39.225993357","2026-05-19T04:16:44.185855519","10.1090/s0025-5718-1985-0771029-9","W2061172735","Global error estimates in L 2 ( Ω ) {L^2}(\\Omega ) , L ∞ ( Ω ) {L^\\infty }(\\Omega ) , and H − s ( Ω ) {H^{ - s}}(\\Omega ) , Ω \\Omega in R 2 {{\\mathbf {R}}^2} or R 3 {{\\mathbf {R}}^3} , are derived for a mixed finite element method for the Dirichlet problem for the elliptic operator L p = − div ⁡ ( a g r a d p + b p ) + c p Lp = - \\operatorname {div}(a\\;{\\mathbf {grad}}\\;p + {\\mathbf {b}}p) + cp based on the Raviart-Thomas-Nedelec space V ","1985-01-01",1985,"Mathematics of Computation",473,[181,222,182],"paper_W1972892940","Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory","{\"openalex\":\"W1972892940\",\"doi\":\"10.1137/0521046\"}","2026-05-15T11:52:03.364554012","2026-05-21T08:29:56.267016859","10.1137/0521046","W1972892940","A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter $\\epsilon $ representing the size of the matrix blocks. This scaling preserves the physics of the flow in the matrix as $\\epsilon $ tends to zero. An effective macroscopic limit model is obtained that includes the usual Darcy equations in the matrix blocks and a similar equation for the fracture system that contains a term representing a source of fluid from the matrix. The convergence is shown by extracting weak limits in appropriate Hilbert spaces. A dilation operator is utilized to see the otherwise vanishing physics in the matrix blocks as $\\epsilon $ tends to zero.","1990-07-01",1990,"SIAM Journal on Mathematical Analysis",608,[182,286,287],"Hydraulic Fracturing and Reservoir Analysis","Groundwater flow and contamination studies",{"_59":289,"_61":290},[],[291],{"_64":292,"_66":293,"_68":294,"_70":295},1784333077511,{"_73":297,"_75":76,"_77":292,"_78":-5,"_79":26,"_80":26,"_81":26,"_82":-5,"_83":-5,"_84":85,"_35":86,"_87":88},[72,296],"[\"portal\",\"industries\"]","industries",[298,299,300,301,302,303,304,305,306,307,308,309],{"_15":371,"_29":372,"_31":-5,"_32":373,"_33":374,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":375,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":372,"_58":374},{"_15":367,"_29":368,"_31":-5,"_32":-5,"_33":369,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":370,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":368,"_58":369},{"_15":361,"_29":362,"_31":-5,"_32":363,"_33":364,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":365,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":362,"_58":364},{"_15":357,"_29":358,"_31":-5,"_32":-5,"_33":359,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":360,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":358,"_58":359},{"_15":353,"_29":354,"_31":-5,"_32":-5,"_33":355,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":356,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":354,"_58":355},{"_15":347,"_29":348,"_31":-5,"_32":349,"_33":350,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":351,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":348,"_58":350},{"_15":342,"_29":343,"_31":-5,"_32":-5,"_33":344,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":345,"_322":26,"_323":346,"_324":26,"_325":-5,"_57":343,"_58":344},{"_15":338,"_29":339,"_31":-5,"_32":-5,"_33":340,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":341,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":339,"_58":340},{"_15":334,"_29":335,"_31":-5,"_32":-5,"_33":336,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":337,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":335,"_58":336},{"_15":330,"_29":331,"_31":-5,"_32":-5,"_33":332,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":333,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":331,"_58":332},{"_15":326,"_29":327,"_31":-5,"_32":-5,"_33":328,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":329,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":327,"_58":328},{"_15":310,"_29":311,"_31":-5,"_32":-5,"_33":312,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":313,"_42":-5,"_44":-5,"_314":315,"_316":-5,"_317":76,"_318":319,"_320":321,"_322":26,"_323":85,"_324":26,"_325":-5,"_57":311,"_58":312},"tax_ind_smartphone","智能手机","Smartphone","manual","taxonomyType","INDUSTRY","code","level","parentId","tax_ind_root","path","科技行业/智能手机","sortOrder","isLeaf","entityCount","children","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算",true,"tax_ind_blockchain","区块链",[352],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[366],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[376,377],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_380":24},"SITE_BASE_URL"]

Jim Douglas 人物

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