{"id":544,"date":"2018-08-16T13:17:30","date_gmt":"2018-08-16T16:17:30","guid":{"rendered":"http:\/\/blog.ufes.br\/isaacsantos\/?page_id=544"},"modified":"2020-03-03T22:19:34","modified_gmt":"2020-03-04T01:19:34","slug":"metodos-de-elementos-finitos-para-equacoes-de-navier-stokes-incompressiveis","status":"publish","type":"page","link":"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/metodos-de-elementos-finitos-para-equacoes-de-navier-stokes-incompressiveis\/","title":{"rendered":"M\u00e9todos de elementos finitos para equa\u00e7\u00f5es de Navier-Stokes incompress\u00edveis &#8211; 2018\/2"},"content":{"rendered":"<h1><span style=\"color: #ff0000\"><strong>Curso<\/strong>:<\/span><\/h1>\n<p>Mestrado e Doutorado em Ci\u00eancia da Computa\u00e7\u00e3o (Per\u00edodo 2018\/2)<\/p>\n<h1><span style=\"color: #ff0000\"><strong>Hor\u00e1rio das aulas<\/strong>:<\/span><\/h1>\n<p>sexta feira: 13:00 &#8211; 17:00 horas &#8211;<\/p>\n<h2><strong>Programa da disciplina<\/strong>:<\/h2>\n<ol>\n<li><strong>Equa\u00e7\u00f5es de Navier-Stokes<\/strong>\n<ol>\n<li>Dedu\u00e7\u00e3o das equa\u00e7\u00f5es de Navier-Stokes incompress\u00edveis<\/li>\n<li>Descri\u00e7\u00e3o do modelo matem\u00e1tico<\/li>\n<li>Formula\u00e7\u00e3o variacional (ou fraca) do modelo matem\u00e1tico<\/li>\n<\/ol>\n<\/li>\n<li><strong>Problema de Stokes<\/strong>\n<ol>\n<li>O problema de ponto de sela linear<\/li>\n<li>A condi\u00e7\u00e3o Inf-Sup<\/li>\n<li>M\u00e9todo de elementos finitos (MEF) para problemas de ponto de sela linear<\/li>\n<li>MEF para o problema de Stokes<\/li>\n<li>Formula\u00e7\u00f5es estabilizadas para o problema de Stokes<\/li>\n<li>Implementa\u00e7\u00e3o computacional<\/li>\n<\/ol>\n<\/li>\n<li><strong>Equa\u00e7\u00f5es de Navier-Stokes Estacion\u00e1rias<\/strong>\n<ol>\n<li>Discretiza\u00e7\u00e3o do termo convectivo<\/li>\n<li>Solu\u00e7\u00e3o iterativa: m\u00e9todos do ponto fixo e de Newton<\/li>\n<li>Formula\u00e7\u00f5es estabilizadas do tipo SUPG\/PSPG<\/li>\n<\/ol>\n<ol>\n<li>Formula\u00e7\u00f5es multiescalas\/submalhas<\/li>\n<li>Implementa\u00e7\u00e3o computacional<\/li>\n<\/ol>\n<\/li>\n<li><strong>Equa\u00e7\u00f5es de Navier-Stokes Transientes<\/strong>\n<ol>\n<li>M\u00e9todos de avan\u00e7o no tempo<\/li>\n<li>M\u00e9todos de proje\u00e7\u00e3o<\/li>\n<li>Implementa\u00e7\u00e3o computacional<\/li>\n<\/ol>\n<\/li>\n<li><strong>Introdu\u00e7\u00e3o \u00e0 Turbul\u00eancia<\/strong>\n<ol>\n<li>Modelos de turbul\u00eancia<\/li>\n<li>Implementa\u00e7\u00e3o computacional<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><!--more--><\/p>\n<h1><a href=\"http:\/\/www.claymath.org\/millennium-problems\/navier%E2%80%93stokes-equation\"><span style=\"color: #ff0000\">Pr\u00eamio de 1 milh\u00e3o de dolares<\/span><\/a><\/h1>\n<h1><span style=\"color: #ff0000\">Notas de aula<\/span><\/h1>\n<p>Abaixo est\u00e3o listadas algumas notas de aulas.<\/p>\n<ul>\n<li><a href=\"http:\/\/blog.ufes.br\/isaacsantos\/files\/2018\/08\/FEM-NS_2018_2_PARTE1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Dedu\u00e7\u00e3o das equa\u00e7\u00f5es de Navier-Stokes incompress\u00edveis<\/a><\/li>\n<li><a href=\"http:\/\/blog.ufes.br\/isaacsantos\/files\/2018\/08\/FEM-NS_2018_2_PARTE2_FormVariacional.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Formula\u00e7\u00e3o variacional (ou fraca) do modelo matem\u00e1tico<\/a><\/li>\n<li><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\">Software e Linguagens de programa\u00e7\u00e3o<\/span><\/h1>\n<ol>\n<li><a href=\"https:\/\/www.mathworks.com\/help\/pde\/?requestedDomain=www.mathworks.com\" target=\"_blank\" rel=\"noopener noreferrer\">Matlab (PDE-tool box)<\/a> ou <a href=\"https:\/\/www.gnu.org\/software\/octave\/\" target=\"_blank\" rel=\"noopener noreferrer\">Octave<\/a><\/li>\n<li><a href=\"http:\/\/www.freefem.org\/\" target=\"_blank\" rel=\"noopener noreferrer\">FreeFem++<\/a><\/li>\n<li><a href=\"https:\/\/fenicsproject.org\/\" target=\"_blank\" rel=\"noopener noreferrer\">Fenics<\/a><\/li>\n<li><a href=\"https:\/\/wiki.octave.org\/Fem-fenics\" target=\"_blank\" rel=\"noopener noreferrer\">Fem-Fenics<\/a><\/li>\n<\/ol>\n<h1><span style=\"color: #ff0000\">Geradores de Malhas<\/span><\/h1>\n<ol>\n<li><a href=\"http:\/\/persson.berkeley.edu\/distmesh\/\">DistMesh &#8211; A Simple Mesh Generator in MATLAB<\/a><\/li>\n<li><a href=\"http:\/\/www.cs.cmu.edu\/~quake\/triangle.html\" target=\"_blank\" rel=\"noopener noreferrer\">Triangle &#8211;&nbsp;A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator<\/a><\/li>\n<li><a href=\"https:\/\/inf.ufes.br\/~luciac\/fem\/Gera_Malha.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Easymes, showmesh e paraview (Ramoni Z. Sedano)<\/a><\/li>\n<\/ol>\n<h1><span style=\"color: #ff0000\">Avalia\u00e7\u00e3o<\/span><\/h1>\n<ul>\n<li>provas, listas de exerc\u00edcios, semin\u00e1rios e trabalhos computacionais\n<ol>\n<li><a href=\"http:\/\/blog.ufes.br\/isaacsantos\/files\/2018\/08\/Lista_1_MEF-NS_2018-2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Lista 1<\/a> (Dedu\u00e7\u00e3o das equa\u00e7\u00f5es de NS incompress\u00edveis) &#8211; entregar dia 31\/08<\/li>\n<li><a href=\"http:\/\/blog.ufes.br\/isaacsantos\/files\/2018\/08\/Lista_2_MEF-NS_2018-2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Lista 2<\/a> &#8211; entregar dia 14\/09<\/li>\n<li>Lista 3 &#8211; entregar dia 28\/09<\/li>\n<li>Lista 4 &#8211; entregar dia 11\/10<\/li>\n<li>Lista 5 &#8211; entregar dia 26\/10<\/li>\n<li>Lista 6 &#8211; entregar dia 09\/11<\/li>\n<li>Lista 7 &#8211; entregar dia 23\/11<\/li>\n<li>Lista 8 &#8211; entregar dia 07\/12<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\">Links interessantes<\/span><\/h1>\n<ol>\n<li><a href=\"http:\/\/persson.berkeley.edu\/distmesh\/\">DistMesh &#8211; A Simple Mesh Generator in MATLAB<\/a><\/li>\n<li><a href=\"http:\/\/Per-Olof Persson, UC Berkeley Mathematics\" target=\"_blank\" rel=\"noopener noreferrer\">Filmes\/simula\u00e7\u00f5es Num\u00e9ricas<\/a> (Prof. Per-Olof Persson, UC Berkeley Mathematics)<\/li>\n<li><a href=\"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/pos-graduacao\/curso-de-verao-lncc-2018\/\" target=\"_blank\" rel=\"noopener noreferrer\">Curso Introdu\u00e7\u00e3o ao MEF<\/a> (Prof. Isaac P. Santos &#8211; LNCC 2018)<\/li>\n<li><a href=\"https:\/\/www.kth.se\/social\/files\/542e7c13f2765401b7da59e3\/robin.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">MEF com condi\u00e7\u00f5es de contorno de Robin &#8211; 1D<\/a><\/li>\n<li><a href=\"https:\/\/www.kth.se\/social\/files\/542e7c32f276547790f96040\/robin_2D.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">MEF com condi\u00e7\u00f5es de contorno de Robin &#8211; 2D<\/a><\/li>\n<\/ol>\n<h1><span style=\"color: #ff0000\">Refer\u00eancias Bibliogr\u00e1ficas<\/span><\/h1>\n<ol>\n<li>Larson, M. G. and Bengzon, F. <a href=\"http:\/\/www.springer.com\/la\/book\/9783642332869\" target=\"_blank\" rel=\"noopener noreferrer\"><em>The Finite Element Method: Theory, Implementation, and Applications<\/em><\/a>. Springer, 2013<\/li>\n<li>\n<div>Volker J. <em><a href=\"https:\/\/www.springer.com\/us\/book\/9783319457499\" target=\"_blank\" rel=\"noopener noreferrer\">Finite Element Methods for Incompressible Flow Problems<\/a><\/em>. Springer, 2016.<\/div>\n<\/li>\n<li>Turek, S. <em><a href=\"https:\/\/www.springer.com\/la\/book\/9783642635731\" target=\"_blank\" rel=\"noopener noreferrer\">Efficient Solvers for Incompressible Flow Problems: An Algorithmic and<\/a><\/em><br \/>\n<a href=\"https:\/\/www.springer.com\/la\/book\/9783642635731\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Computational Approach<\/em><\/a>. Springer, 1999.<\/li>\n<li>Elman, H. Silvester, D. J. and Wathen, A. J. <a href=\"https:\/\/www.amazon.com\/Finite-Elements-Fast-Iterative-Solvers\/dp\/0198528671\" target=\"_blank\" rel=\"noopener noreferrer\">Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics<\/a>.&nbsp; Oxford University Press, 2005.<\/li>\n<li>Quarteroni, A. <a href=\"https:\/\/www.springer.com\/la\/book\/9788847058835\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Numerical Models for Differential Problems<\/em><\/a>. Springer, 2009.<\/li>\n<li>Johnson, C. <a href=\"https:\/\/www.amazon.com\/Numerical-Solution-Differential-Equations-Mathematics\/dp\/048646900X\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Numerical Solution of Partial Differential Equations by the Finite Element Method<\/em><\/a>. Dover Publication, 2009.<\/li>\n<li>Donea, J. and Huerta, A. <em><a href=\"http:\/\/www.wiley.com\/WileyCDA\/WileyTitle\/productCd-0471496669.html\" target=\"_blank\" rel=\"noopener noreferrer\">Finite Element Methods for Flow Problems<\/a>.<\/em>&nbsp;John Wiley &amp; Sons, 2003.<\/li>\n<li>A. Quarteroni and A. Valli. <a href=\"https:\/\/www.springer.com\/us\/book\/9783540852674\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Numerical Approximation of Partial Differential Equations<\/em><\/a>. Springer, 1994.<\/li>\n<li>Girault V. and Raviart, P-A. <a href=\"https:\/\/www.springer.com\/us\/book\/9783642648885\" target=\"_blank\" rel=\"noopener noreferrer\">Finite Element Methods for Navier-Stokes Equations &#8211; Theory and Algorithms<\/a>. Springer, 1986.<\/li>\n<li>M. Gunzburger. <em><a href=\"https:\/\/www.elsevier.com\/books\/finite-element-methods-for-viscous-incompressible-flows\/gunzburger\/978-0-12-307350-1\" target=\"_blank\" rel=\"noopener noreferrer\">Finite Element Method for Viscous Incompressible Flows<\/a><\/em>. Academic press, 1989.<\/li>\n<li>Mark S. Gockenbach.&nbsp;<a href=\"http:\/\/bookstore.siam.org\/ot97\/\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Understanding and implementing the finite element method<\/em><\/a>.&nbsp;Society for Industrial and Applied Mathematics (SIAM), 2006.<\/li>\n<li>A. Chorin and J.E. Marsden. A Mathematical Introduction to Fluid Mechanics. Springer, 1999.<\/li>\n<li>\n<div>A. Ern and J. L. Guermond. <a href=\"https:\/\/www.springer.com\/la\/book\/9780387205748\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Theory and Practice of Finite Elements<\/em><\/a>. Springer, 2004.<\/div>\n<\/li>\n<li><a href=\"http:\/\/www.freefem.org\/ff++\/ftp\/freefem++doc.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Manual Freefem++<\/a> http:\/\/www.freefem.org\/ff++\/<\/li>\n<li>A. Logg, K. Mardal and G. N. Wells. <a href=\"https:\/\/fenicsproject.org\/\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Automated solution of differential equations by the finite element method<\/em><\/a> &#8211; The FEniCs Book. Springer, 2012.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Curso: Mestrado e Doutorado em Ci\u00eancia da Computa\u00e7\u00e3o (Per\u00edodo 2018\/2) Hor\u00e1rio das aulas: sexta feira: 13:00 &#8211; 17:00 horas &#8211; Programa da disciplina: Equa\u00e7\u00f5es de Navier-Stokes Dedu\u00e7\u00e3o das equa\u00e7\u00f5es de Navier-Stokes incompress\u00edveis Descri\u00e7\u00e3o do modelo matem\u00e1tico Formula\u00e7\u00e3o variacional (ou fraca) &hellip; <a href=\"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/metodos-de-elementos-finitos-para-equacoes-de-navier-stokes-incompressiveis\/\">Continue lendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":279,"featured_media":0,"parent":73,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-544","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"post-thumbnail":false,"large-feature":false,"small-feature":false},"uagb_author_info":{"display_name":"Isaac","author_link":"https:\/\/blog.ufes.br\/isaacsantos\/author\/isaac_pinheiro-dos-santos\/"},"uagb_comment_info":0,"uagb_excerpt":"Curso: Mestrado e Doutorado em Ci\u00eancia da Computa\u00e7\u00e3o (Per\u00edodo 2018\/2) Hor\u00e1rio das aulas: sexta feira: 13:00 &#8211; 17:00 horas &#8211; Programa da disciplina: Equa\u00e7\u00f5es de Navier-Stokes Dedu\u00e7\u00e3o das equa\u00e7\u00f5es de Navier-Stokes incompress\u00edveis Descri\u00e7\u00e3o do modelo matem\u00e1tico Formula\u00e7\u00e3o variacional (ou fraca) &hellip; Continue lendo &rarr;","_links":{"self":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/544","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/users\/279"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/comments?post=544"}],"version-history":[{"count":25,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/544\/revisions"}],"predecessor-version":[{"id":688,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/544\/revisions\/688"}],"up":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/73"}],"wp:attachment":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/media?parent=544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}