{"id":1424,"date":"2021-10-22T11:32:02","date_gmt":"2021-10-22T09:32:02","guid":{"rendered":"https:\/\/ecoles-cea-edf-inria.fr\/?page_id=1424"},"modified":"2021-10-22T11:32:02","modified_gmt":"2021-10-22T09:32:02","slug":"ecole-analyse-numerique-2022","status":"publish","type":"page","link":"https:\/\/ecoles-cea-edf-inria.fr\/en\/history\/ecole-analyse-numerique-2022\/","title":{"rendered":"Numerical analysis school 2022"},"content":{"rendered":"<div id=\"headerredbloc\">\nNumerical analysis school 2022: contents, program, dates, practical information.\n<\/div>\n<div id=\"initiative\">\n<h1 class=\"textebleu\">2022 summer school on numerical analysis<\/h1>\n<h2>Certification of errors in numerical simulations<\/h2>\n<h3><em>Preservation of invariants by post-processing and adaptivity (mesh, scheme, solvers, model) for industrial needs<\/em><\/h3>\n<div style=\"width: 65%;padding: 0 10px 0 0;float: left\">\n<h4><span style=\"color: #ff0000\">Contents<\/span><\/h4>\n<h3>Certification of errors in numerical simulations<\/h3>\n<p>Numerical simulation of partial differential equations has become an essential tool for finding approximate solutions to physical problems. It leads to several important questions:<\/p>\n<ul>\n<li>What is the <strong>error<\/strong> in the <strong>numerical approximation<\/strong>?<\/li>\n<li>Can we <strong>certify the result<\/strong>, give a safety margin?<\/li>\n<li>Can we estimate the error in <strong>quantities of interest<\/strong> identified by the user (point value of the solution, flow through a part of the boundary)?<\/li>\n<li>Can we have this information for an <strong>affordable cost<\/strong>, much smaller compared to the cost of the numerical simulation itself?<\/li>\n<\/ul>\n<p>It is the theory of <strong>a posteriori error estimates<\/strong> which makes it possible to give affirmative answers to these questions. Exposing its latest advances, in detail for simple model problems, will be the central pillar of the proposed summer school.<\/p>\n<h3>Preservation of invariants by post-processing<\/h3>\n<p>The peculiarity of some a posteriori approaches is that they actually provide an <strong>improvement of the numerical approximation<\/strong>. These improvements make it possible to satisfy another highly desired property in numerical simulations: the <strong>preservation of invariants<\/strong>. For example, one can find a locally conservative field for a scheme non-conservative by construction via a <strong>local postprocessing<\/strong> which is already part of the a posteriori error evaluation. One day in the school will be devoted to this subject.<\/p>\n<h3>Adaptivity of mesh, scheme, solvers, and model<\/h3>\n<p>The theory of posteriori error estimates is also the basis of the concept of <strong>adaptivity<\/strong> of <strong>mesh<\/strong>, but also more broadly, including the <strong>scheme<\/strong>, the <strong>linear and nonlinear solvers<\/strong>, or the <strong>model<\/strong>. To give the participants an idea of the power of such an adaptivity, scientific seminars and industrial experiences will discuss these aspects.<\/p>\n<p><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/10\/Ecole_2022_analyse_num_en.pdf\">Detailed description<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/p>\n<\/div>\n<div style=\"width: 35%;padding: 0 10px 0 30px;float: left\">\n<h4><span style=\"color: #ff0000\">Practical information<\/span><\/h4>\n<h3>Date<\/h3>\n<p>June 27 &ndash; July 1, 2022<\/p>\n<h3>Place<\/h3>\n<p>EDF Lab<br \/>\nParis-Saclay<br \/>\nBoulevard Gaspard Monge<br \/>\n91120 Palaiseau<\/p>\n<h3>Registration<\/h3>\n<p>If you wish to join, please fill the <a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/11\/registration_form_numerical_analysis_2022.doc\">registration form <img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/10\/word-e1635282179335.png\" alt=\"Word icon\" width=\"70\" \/> <\/a> and send it before <strong>June, 3, 2022<\/strong> to <a href=\"mailto:regis.vizet@cea.fr\">R\u00e9gis Vizet<\/a>.<\/p>\n<h3>Contacts<\/h3>\n<p><strong>Summer schools secretary<\/strong><br \/>\n<a href=\"mailto:regis.vizet@cea.fr\">R\u00e9gis Vizet<\/a> &#8211; CEA<br \/>\ntel: 01 69 26 47 45<br \/>\nFax: 01 69 26 70 05<\/p>\n<p><strong>Coordinators of the numerical analysis 2022 school<\/strong><br \/>\n<a href=\"mailto:mickael.abbas@edf.fr\">Micka\u00ebl Abbas<\/a><br \/>\n<a href=\"mailto:martin.vohralik@inria.fr\">Martin Vohral\u00edk<\/a><\/p>\n<h3>Registration fees (pre-tax price)<\/h3>\n<p>CEA, EDF, industry: 1200 euros<br \/>\nAcademia \/ university &amp; public research: 600 euros<br \/>\nPh.D. students (a limited number): 300 euros<\/p>\n<\/div>\n<div style=\"clear: both\"><\/div>\n<h4><span style=\"color: #ff0000\">Program<\/span><\/h4>\n<table>\n<tr>\n<th><\/th>\n<th style=\"width:19%\">Monday, June 27<\/th>\n<th style=\"width:19%\">Tuesday, June 28<\/th>\n<th style=\"width:20%\">Wednesday, June 29<\/th>\n<th style=\"width:19%\">Thursday, June 30<\/th>\n<th style=\"width:30%\">Friday, July 1<\/th>\n<\/tr>\n<tr>\n<th><\/th>\n<th>Certification of errors<\/th>\n<th>Nonlinear and evolutive problems, identification of error components<\/th>\n<th>Errors in quantities of interest, model adaptivity, multiscale<\/th>\n<th>Convergence and optimality by mesh adaptivity<\/th>\n<th>Industrial employment<\/th>\n<\/tr>\n<tr>\n<td>8h30-9h30<\/td>\n<td>Breakfast coffee<\/td>\n<td>Breakfast coffee<\/td>\n<td>Breakfast coffee<\/td>\n<td>Breakfast coffee<\/td>\n<td>Breakfast coffee<\/td>\n<\/tr>\n<tr>\n<td>9h30-12h<\/td>\n<td>Lectures<br \/> <a href=\"http:\/\/cermics.enpc.fr\/~ern\/home.html\"><strong>Alexandre Ern<\/strong><\/a> (Ecole des Ponts)<\/td>\n<td>Lectures<br \/> <a href=\"http:\/\/cermics.enpc.fr\/~ern\/home.html\"><strong>Alexandre Ern<\/strong><\/a> (Ecole des Ponts)<\/td>\n<td>Lectures<br \/> <a href=\"https:\/\/w3.lmt.ens-cachan.fr\/site\/php_perso\/perso_page_lmt.php?nom=CHAMOIN\"><strong>Ludovic Chamoin<\/strong> <\/a> (ENS Paris Saclay)<a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Chamoin.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Lectures<br \/> <a href=\"https:\/\/www.unimi.it\/en\/ugov\/person\/andreas-veeser\"><strong>Andreas Veeser<\/strong><\/a> (Universit\u00e0 degli Studi di Milano)<a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Veeser.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Examples<br \/>9h30 <strong>Fran\u00e7ois Madiot<\/strong> (CEA): <em>A posteriori error estimates for mixed finite element discretizations of the neutron diffusion equations<\/em><br \/>11h <strong>Pascal Omnes<\/strong> (CEA): <em>Adaptive simulations in incompressible fluid dynamics: issues and needs<\/em><\/td>\n<\/tr>\n<tr>\n<td>12h-14h<\/td>\n<td>Lunch<\/td>\n<td>Lunch<\/td>\n<td>Lunch<\/td>\n<td>Lunch<\/td>\n<td>Lunch<\/td>\n<\/tr>\n<tr>\n<td>14h-16h<\/td>\n<td>Computer tutorials<br \/><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/TP1.pdf\">Announcement and correction<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a> <\/p>\n<p><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP1.edp\">FreeFem++ script<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Computer tutorials<br \/><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/TP2.pdf\">Announcement and correction<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/p>\n<p><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP2.edp\">FreeFem++ script<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><br \/><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP2_plotter.edp\">plotter<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Computer tutorials<br \/><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/TP3.pdf\">Announcement and correction<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/p>\n<p><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP3.edp\">FreeFem++ script<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Computer tutorials<br \/><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/TP4.pdf\">Announcement and correction<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/p>\n<p><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP4.edp\">FreeFem++ script<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><br \/><a href=\"https:\/\/medsci-sites.inria.fr\/ecoles-cea-edf-inria\/wp-content\/uploads\/sites\/10\/2022\/07\/TP4plotter.edp\">plotter<img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/06\/FF.png\" alt=\"FF icon\" width=\"70\" \/> <\/a><\/td>\n<td>Examples<br \/>14h <strong>Romain Le Tellier<\/strong> (CEA): <em>hp\u2212AMR applied to the neutron transport equation discretized by a discontinuous Galerkin upwind scheme<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/LeTellier.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><br \/>15h <strong>Soleiman Yousef<\/strong> (IFPEN): <em>Reservoir simulator runtime enhancement based on a posteriori error estimation techniques<\/em> <\/td>\n<\/tr>\n<tr>\n<td>16h-16h30<\/td>\n<td>Coffee break<\/td>\n<td>Coffee break<\/td>\n<td>Coffee break<\/td>\n<td>Coffee break<\/td>\n<td>Coffee break<\/td>\n<\/tr>\n<tr>\n<td>16h30-18h<\/td>\n<td>Scientific seminars<\/td>\n<td>Scientific seminars<\/td>\n<td>Scientific seminars<\/td>\n<td>Scientific seminars<\/td>\n<td>Discussion, conclusions, and perspectives<\/td>\n<\/tr>\n<tr>\n<td>16h30<\/td>\n<td><strong>Th\u00e9ophile Chaumont-Frelet<\/strong> (Inria Sophia Antipolis): <em>A posteriori error estimation via flux equilibration for magnetostatic problems<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/ChaumontFrelet.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a> <\/td>\n<td><strong>Pierre Gosselet<\/strong> (Universit\u00e9 de Lille): <em>Parallel error estimation for primal and dual domain decomposition methods<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Gosselet.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td><strong>Valentine Rey<\/strong> (Universit\u00e9 de Nantes): <em>Error estimation in reliability analysis : multi-fidelity meta-models for the estimation of probability of failure<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Rey.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td><strong>Dirk Praetorius<\/strong> (Vienna University of Technology): <em>On quasi-optimal computational costs of adaptive FEM<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Praetorius.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<\/tr>\n<tr>\n<td>17h15<\/td>\n<td> <strong>S\u00f4nia M. Gomes<\/strong> (Universidade Estadual de Campinas): <em>A posteriori error estimator for a multiscale hybrid mixed method applied to Darcy&#8217;s flows<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Gomes.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td> <strong>Koondanibha Mitra<\/strong> (Hasselt University): <em>Reliable, efficient, and robust a posteriori estimates for nonlinear elliptic problems<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Mitra.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td><strong>Fr\u00e9d\u00e9ric Legoll<\/strong> (\u00c9cole des Ponts ParisTech): <em>Numerical simulations using the multiscale finite element method: a posteriori estimates and mesh adaptivity<\/em><a href=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2022\/07\/Legoll.pdf\"><img decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/ecoles-cea-edf-inria.fr\/files\/2021\/09\/pdficon-e1631999820667.png\" alt=\"PDF icon\" width=\"70\" \/> <\/a><\/td>\n<td><strong>Roland Becker<\/strong> (Universit\u00e9 de Pau et des Pays de l\u2019Adour): <em>Adaptive FEM for parameter identification problems<\/em><\/td>\n<\/tr>\n<\/table>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Numerical analysis school 2022: contents, program, dates, practical information. 2022 summer school on numerical analysis Certification of errors in numerical simulations Preservation of invariants by &hellip;<\/p>\n","protected":false},"author":505,"featured_media":1176,"parent":1159,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1424","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/pages\/1424","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/users\/505"}],"replies":[{"embeddable":true,"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/comments?post=1424"}],"version-history":[{"count":0,"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/pages\/1424\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/pages\/1159"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/media\/1176"}],"wp:attachment":[{"href":"https:\/\/ecoles-cea-edf-inria.fr\/en\/wp-json\/wp\/v2\/media?parent=1424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}