{"id":429,"date":"2017-10-10T15:19:33","date_gmt":"2017-10-10T13:19:33","guid":{"rendered":"http:\/\/project.inria.fr\/gatipor\/?p=429"},"modified":"2021-12-02T19:03:14","modified_gmt":"2021-12-02T18:03:14","slug":"local-space-time-efficiency","status":"publish","type":"post","link":"https:\/\/project.inria.fr\/gatipor\/local-space-time-efficiency\/","title":{"rendered":"Local space-time efficiency for parabolic problems"},"content":{"rendered":"<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td><div id=\"attachment_140\" style=\"width: 610px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"846\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes-1024x846.png\" alt=\"meshes\" class=\"alignnone size-large wp-image-433\" srcset=\"https:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes-1024x846.png 1024w, https:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes-300x248.png 300w, https:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes-768x634.png 768w, https:\/\/project.inria.fr\/gatipor\/files\/2017\/10\/meshes-150x124.png 150w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\">Mesh coarsening and refinement treated by local problems on a common submesh<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Main results<\/strong> (heat equation):<\/p>\n<ul>\n<li>inf-sup <strong>equality<\/strong> with constant 1;<\/li>\n<li>any order conforming continuous Galerkin discretization in space;<\/li>\n<li>any order discontinuous Galerkin discretization in time;<\/li>\n<li>guranteed reliability (upper bound);<\/li>\n<li>efficiency <strong>local<\/strong> with respect to both <strong>space<\/strong> and <strong>time<\/strong>;<\/li>\n<li><strong>robustness<\/strong> with respect to <strong>polynomial degrees<\/strong> both in space and time;<\/li>\n<li><strong>arbitrary<\/strong> space mesh <strong>refinement<\/strong> and <strong>coarsening<\/strong> between time steps (no transition condition);<\/li>\n<li><strong>equivalence<\/strong> between <strong>global<\/strong> and <strong>local<\/strong> norms.<\/li>\n<\/ul>\n<p>Details: <a href=\"https:\/\/who.rocq.inria.fr\/Martin.Vohralik\/Files\/Pub_SINUM_17_b.pdf\">paper<\/a> with Alexandre Ern and Iain Smears and <a href=\"https:\/\/who.rocq.inria.fr\/Martin.Vohralik\/Files\/Exp_MoRe_17.pdf\">presentation<\/a>; see also <a href=\"https:\/\/academic.oup.com\/imajna\/advance-article\/doi\/10.1093\/imanum\/dry035\/5041990\">paper<\/a> (<a href=\"https:\/\/hal.inria.fr\/hal-01489721\">preprint<\/a>) in the energy norm setting.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Main results (heat equation): inf-sup equality with constant 1; any order conforming continuous Galerkin discretization in space; any order discontinuous Galerkin discretization in time; guranteed reliability (upper bound); efficiency local with respect to both space and time; robustness with respect to polynomial degrees both in space and time; arbitrary space\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/gatipor\/local-space-time-efficiency\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":932,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-429","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/users\/932"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/comments?post=429"}],"version-history":[{"count":21,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/429\/revisions"}],"predecessor-version":[{"id":1043,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/429\/revisions\/1043"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media?parent=429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/categories?post=429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/tags?post=429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}