{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:51:16Z","timestamp":1775055076554,"version":"3.50.1"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319986531","type":"print"},{"value":"9783319986548","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-99639-4_5","type":"book-chapter","created":{"date-parts":[[2018,8,22]],"date-time":"2018-08-22T15:43:34Z","timestamp":1534952614000},"page":"67-81","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations"],"prefix":"10.1007","author":[{"given":"Yury A.","family":"Blinkov","sequence":"first","affiliation":[]},{"given":"Vladimir P.","family":"Gerdt","sequence":"additional","affiliation":[]},{"given":"Dmitry A.","family":"Lyakhov","sequence":"additional","affiliation":[]},{"given":"Dominik L.","family":"Michels","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,8,23]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"Adams, W.W., Loustanau, P.: Introduction to Gr\u00f6bner Bases. Graduate Studies in Mathematics, vol. 3, American Mathematical Society, Providence (1994)","DOI":"10.1090\/gsm\/003"},{"key":"5_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/978-3-319-02297-0_4","volume-title":"Computer Algebra in Scientific Computing","author":"P Amodio","year":"2013","unstructured":"Amodio, P., Blinkov, Y., Gerdt, V., La Scala, R.: On consistency of finite difference approximations to the Navier-Stokes equations. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 46\u201360. Springer, Cham (2013). https:\/\/doi.org\/10.1007\/978-3-319-02297-0_4"},{"key":"5_CR3","first-page":"408","volume":"314","author":"P Amodio","year":"2017","unstructured":"Amodio, P., Blinkov, Y.A., Gerdt, V.P., La Scala, R.: Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations. Appl. Math. Comput. 314, 408\u2013421 (2017)","journal-title":"Appl. Math. Comput."},{"key":"5_CR4","unstructured":"Blinkov, Y.A., Cid, C.F., Gerdt, V.P., Plesken, W., Robertz, D.: The MAPLE package Janet: II. Linear partial differential equations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) Proceedings of 6th International Workshop on Computer Algebra in Scientific Computing, CASC 2003, pp. 41\u201354. Technische Universit\u00e4t M\u00fcnchen (2003). Package Janet is freely available on the web page http:\/\/wwwb.math.rwth-aachen.de\/Janet\/"},{"issue":"10","key":"5_CR5","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1021\/ie50286a020","volume":"25","author":"GH Fancher","year":"1933","unstructured":"Fancher, G.H., Lewis, J.A.: Flow of simple fluids through porous materials. Indus. Eng. Chem. Res. 25(10), 1139\u20131147 (1933)","journal-title":"Indus. Eng. Chem. Res."},{"key":"5_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032602","volume-title":"Computer-Aided Analysis of Difference Schemes for Partial Differential Equations","author":"VG Ganzha","year":"1996","unstructured":"Ganzha, V.G., Vorozhtsov, E.V.: Computer-Aided Analysis of Difference Schemes for Partial Differential Equations. Wiley, New York (1996)"},{"key":"5_CR7","first-page":"051","volume":"2","author":"VP Gerdt","year":"2006","unstructured":"Gerdt, V.P., Blinkov, Y.A., Mozzhilkin, V.V.: Gr\u00f6bner bases and generation of difference schemes for partial differential equations. SIGMA 2, 051 (2006)","journal-title":"SIGMA"},{"key":"5_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1007\/978-3-642-04103-7_10","volume-title":"Computer Algebra in Scientific Computing","author":"VP Gerdt","year":"2009","unstructured":"Gerdt, V.P., Blinkov, Y.A.: Involution and difference schemes for the Navier\u2013Stokes equations. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2009. LNCS, vol. 5743, pp. 94\u2013105. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-04103-7_10"},{"key":"5_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/978-3-642-28212-6_3","volume-title":"Mathematical Modeling and Computational Science","author":"VP Gerdt","year":"2012","unstructured":"Gerdt, V.P.: Consistency analysis of finite difference approximations to PDE systems. In: Adam, G., Bu\u0161a, J., Hnati\u010d, M. (eds.) MMCP 2011. LNCS, vol. 7125, pp. 28\u201342. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28212-6_3"},{"key":"5_CR10","unstructured":"Gerdt, V.P.: Involutive algorithms for computing Gr\u00f6bner bases. In: Cojocaru, S., Pfister, G., Ufnarovski, V. (eds.) Computational Commutative and Non-Commutative Algebraic Geometry, NATO Science Series, pp. 199\u2013225. IOS Press (2005)"},{"key":"5_CR11","unstructured":"Gerdt, V.P., Robertz, D.: Computation of difference Gr\u00f6bner bases. Comput. Sci. J. Moldova 20 2(59), 203\u2013226 (2012). Package LDA is freely available on the web page http:\/\/wwwb.math.rwth-aachen.de\/Janet\/"},{"key":"5_CR12","doi-asserted-by":"crossref","unstructured":"Gerdt, V.P., Robertz, D.: Consistency of finite difference approximations for linear PDE systems and its algorithmic verification. In: Watt, S.M. (ed.) ISSAC 2010, pp. 53\u201359. Association for Computing Machinery, New York (2010)","DOI":"10.1145\/1837934.1837950"},{"key":"5_CR13","doi-asserted-by":"publisher","first-page":"2182","DOI":"10.1063\/1.1761178","volume":"8","author":"FH Harlow","year":"1965","unstructured":"Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182\u20132189 (1965)","journal-title":"Phys. Fluids"},{"key":"5_CR14","unstructured":"Kohr, M., Pop, I.: Viscous Incompressible Flow for Low Reynolds Numbers. Advances in Boundary Elements, vol. 16. WIT Press, Sauthampton (2004)"},{"key":"5_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-6947-5","volume-title":"Difference Algebra. Algebra and Applications","author":"A Levin","year":"2008","unstructured":"Levin, A.: Difference Algebra. Algebra and Applications, vol. 8. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-1-4020-6947-5"},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"Milne-Tompson, L.M.: Theoretical Hydrodynamics, 5th edn. Macmillan Education LTD, Banjul (1968)","DOI":"10.1007\/978-1-349-00517-8"},{"key":"5_CR17","doi-asserted-by":"crossref","unstructured":"Moin, P.: Fundamentals of Engineering Numerical Analysis, 2nd edn. Cambridge University Press, Cambridge (2010)","DOI":"10.1017\/CBO9780511781438"},{"key":"5_CR18","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1006\/jcph.2001.6754","volume":"172","author":"NA Petersson","year":"2001","unstructured":"Petersson, N.A.: Stability of pressure boundary conditions for Stokes and Navier-Stokes equations. J. Comput. Phys. 172, 40\u201370 (2001)","journal-title":"J. Comput. Phys."},{"key":"5_CR19","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01287-7","volume-title":"Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra","author":"WM Seiler","year":"2010","unstructured":"Seiler, W.M.: Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra. Algorithms and Computation in Mathematics, vol. 24. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-01287-7"},{"key":"5_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68983-3","volume-title":"The Method of Differential Approximation","author":"YI Shokin","year":"1983","unstructured":"Shokin, Y.I.: The Method of Differential Approximation. Springer, Berlin (1983)"}],"container-title":["Lecture Notes in Computer Science","Developments in Language Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-99639-4_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T15:37:00Z","timestamp":1571758620000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-99639-4_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319986531","9783319986548"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-99639-4_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]}}}