{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T11:33:36Z","timestamp":1774438416426,"version":"3.50.1"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030268305","type":"print"},{"value":"9783030268312","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","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":[[2019]]},"DOI":"10.1007\/978-3-030-26831-2_28","type":"book-chapter","created":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T23:07:07Z","timestamp":1565824027000},"page":"430-450","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Divergence-Free Method for Solving the Incompressible Navier\u2013Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation"],"prefix":"10.1007","author":[{"given":"Evgenii V.","family":"Vorozhtsov","sequence":"first","affiliation":[]},{"given":"Vasily P.","family":"Shapeev","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,24]]},"reference":[{"key":"28_CR1","unstructured":"Binzubair, H.: Efficient multigrid methods based on improved coarse grid correction techniques. Thesis. Delft Univ. of Technology, Delft, The Netherlands (2009)"},{"key":"28_CR2","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/S0045-7930(98)00002-4","volume":"27","author":"O Botella","year":"1998","unstructured":"Botella, O., Peyret, R.: Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27, 421\u2013433 (1998)","journal-title":"Comput. Fluids"},{"key":"28_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719505","volume-title":"A Multigrid Tutorial","author":"WL Briggs","year":"2000","unstructured":"Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000)","edition":"2"},{"issue":"3","key":"28_CR4","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/0041-5553(64)90253-8","volume":"4","author":"RP Fedorenko","year":"1964","unstructured":"Fedorenko, R.P.: The speed of convergence of one iterative process. USSR Comput. Math. Math. Phys. 4(3), 227\u2013235 (1964)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"28_CR5","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1002\/fld.1650110704","volume":"11","author":"DK Gartling","year":"1990","unstructured":"Gartling, D.K.: A test problem for outflow boundary conditions - flow over a backward-facing step. Int. J. Numer. Methods Fluids 11, 953\u2013967 (1990)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"28_CR6","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1134\/S0965542510100040","volume":"50","author":"VI Isaev","year":"2010","unstructured":"Isaev, V.I., Shapeev, V.P.: High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations. Comput. Math. Math. Phys. 50, 1670\u20131681 (2010)","journal-title":"Comput. Math. Math. Phys."},{"key":"28_CR7","volume-title":"Fundamentals of Grid Generation","author":"P Knupp","year":"1994","unstructured":"Knupp, P., Steinberg, S.: Fundamentals of Grid Generation. CRC Press, Boca Raton (1994)"},{"key":"28_CR8","unstructured":"Krylov, A.N.: On the numerical solution of the equation, which determines in technological questions the frequencies of small oscillations of material systems. Izv. AN SSSR, Otd. matem. i estestv. nauk 4, 491\u2013539 (1931). (in Russian)"},{"key":"28_CR9","unstructured":"Kudryavtseva, I.V., Rykov, S.A., Rykov, S.V., Skobov, E.D.: Optimization Methods in the Examples in the MathCAD 15 Package. Part I, NIU ITMO, St. Petersburg (2014). (in Russian)"},{"key":"28_CR10","doi-asserted-by":"publisher","first-page":"1874","DOI":"10.1137\/080719145","volume":"31","author":"AV Shapeev","year":"2009","unstructured":"Shapeev, A.V., Lin, P.: An asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows. SIAM J. Sci. Comput. 31, 1874\u20131900 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"28_CR11","doi-asserted-by":"publisher","first-page":"01009","DOI":"10.1051\/epjconf\/201610801009","volume":"108","author":"Vasily Shapeev","year":"2016","unstructured":"Shapeev, V.: Collocation and least residuals method and its applications. EPJ Web of Conferences 108, 01009. \n                    https:\/\/doi.org\/10.1051\/epjconf\/201610801009","journal-title":"EPJ Web of Conferences"},{"key":"28_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/978-3-319-02297-0_31","volume-title":"Computer Algebra in Scientific Computing","author":"VP Shapeev","year":"2013","unstructured":"Shapeev, V.P., Vorozhtsov, E.V.: CAS application to the construction of the collocations and least residuals method for the solution of 3D Navier\u2013Stokes equations. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 381\u2013392. Springer, Cham (2013). \n                    https:\/\/doi.org\/10.1007\/978-3-319-02297-0_31"},{"key":"28_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/978-3-642-32973-9_27","volume-title":"Computer Algebra in Scientific Computing","author":"VP Shapeev","year":"2012","unstructured":"Shapeev, V.P., Vorozhtsov, E.V.: Symbolic-numeric implementation of the method of collocations and least squares for 3D Navier\u2013Stokes equations. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2012. LNCS, vol. 7442, pp. 321\u2013333. Springer, Heidelberg (2012). \n                    https:\/\/doi.org\/10.1007\/978-3-642-32973-9_27"},{"key":"28_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/978-3-319-45641-6_30","volume-title":"Computer Algebra in Scientific Computing","author":"VP Shapeev","year":"2016","unstructured":"Shapeev, V.P., Vorozhtsov, E.V.: Symbolic-numerical optimization and realization of the method of collocations and least residuals for solving the Navier\u2013Stokes equations. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2016. LNCS, vol. 9890, pp. 473\u2013488. Springer, Cham (2016). \n                    https:\/\/doi.org\/10.1007\/978-3-319-45641-6_30"},{"key":"28_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1007\/978-3-319-66320-3_25","volume-title":"Computer Algebra in Scientific Computing","author":"VP Shapeev","year":"2017","unstructured":"Shapeev, V.P., Vorozhtsov, E.V.: The method of collocations and least residuals combining the integral form of collocation equations and the matching differential relations at the solution of PDEs. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2017. LNCS, vol. 10490, pp. 346\u2013361. Springer, Cham (2017). \n                    https:\/\/doi.org\/10.1007\/978-3-319-66320-3_25"},{"key":"28_CR16","unstructured":"Sleptsov, A.G.: Collocation-grid solution of elliptic boundary-value problems. Modelirovanie v mekhanike 5(22), 101\u2013126 (1991). (in Russian)"},{"key":"28_CR17","volume-title":"Numerical Grid Generation - Foundations and Applications","author":"JF Thompson","year":"1985","unstructured":"Thompson, J.F., Warsi, Z.U.A., Mastin, C.W.: Numerical Grid Generation - Foundations and Applications. Elsevier Science Publishing Co., New York (1985)"},{"key":"28_CR18","volume-title":"The Mathematica Book","author":"S Wolfram","year":"2003","unstructured":"Wolfram, S.: The Mathematica Book, 5th edn. Wolfram Media, Inc., Champaign (2003)","edition":"5"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-26831-2_28","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T23:09:04Z","timestamp":1565824144000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-26831-2_28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030268305","9783030268312"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-26831-2_28","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"24 July 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Moscow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Russia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.casc.cs.uni-bonn.de\/2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}