{"id":1079,"date":"2021-12-02T20:08:16","date_gmt":"2021-12-02T19:08:16","guid":{"rendered":"http:\/\/project.inria.fr\/gatipor\/?p=1079"},"modified":"2021-12-03T00:26:29","modified_gmt":"2021-12-02T23:26:29","slug":"robust-a-posteriori-error-estimates-for-reactiondiffusion-problems","status":"publish","type":"post","link":"https:\/\/project.inria.fr\/gatipor\/robust-a-posteriori-error-estimates-for-reactiondiffusion-problems\/","title":{"rendered":"Robust a posteriori error estimates for reaction&ndash;diffusion problems"},"content":{"rendered":"<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>\n<div id=\"attachment_140\" style=\"width: 910px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_react.png\"><img decoding=\"async\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_react.png\" alt=\"reaction-diffusion\" width=\"900\" class=\"alignnone size-large wp-image-452\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\">Errors (left) and estimators (right), boundary layer<\/p><\/div><\/td>\n<\/tr>\n<tr>\n<td>\n<div id=\"attachment_140\" style=\"width: 910px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_react_eff.png\"><img decoding=\"async\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_react_eff.png\" alt=\"reaction-diffusion\" width=\"900\" class=\"alignnone size-large wp-image-452\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\">Error, error components, and estimators (left) and effectivity index (right), counter-example for no weights\/submesh<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Main results<\/strong>:<\/p>\n<ul>\n<li> steady linear reaction&ndash;diffusion equation;<\/li>\n<li> arbitrary-order finite element approximation, arbitrary space dimension;<\/li>\n<li> <strong>a posteriori error estimates<\/strong>:\n<ul>\n<li> <strong>guaranteed<\/strong> upper bound in the energy norm;<\/li>\n<li> <strong>local efficiency<\/strong>;<\/li>\n<li> <strong>robustness<\/strong> with respect to <strong>reaction dominance<\/strong>;<\/li>\n<\/ul>\n<\/li>\n<li> <strong>inexpensive construction<\/strong> (weights; no submesh, no combination with residual estimates);<\/li>\n<li> counter-example where estimates with no weights\/submesh\/combination fail;<\/li>\n<li> <strong>explicit bounds<\/strong> for <strong>inverse inequality constants<\/strong> on a <strong>simplex<\/strong>.<\/li>\n<\/ul>\n<p>Details: <a href=\"https:\/\/www.esaim-m2an.org\/articles\/m2an\/abs\/2020\/06\/m2an190182\/m2an190182.html\">paper<\/a> (<a href=\"https:\/\/hal.inria.fr\/hal-01956180\">preprint<\/a>) with Iain Smears, <a href=\"https:\/\/who.rocq.inria.fr\/Martin.Vohralik\/Files\/Exp_corrosion_19.pdf\">presentation<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Main results: steady linear reaction&ndash;diffusion equation; arbitrary-order finite element approximation, arbitrary space dimension; a posteriori error estimates: guaranteed upper bound in the energy norm; local efficiency; robustness with respect to reaction dominance; inexpensive construction (weights; no submesh, no combination with residual estimates); counter-example where estimates with no weights\/submesh\/combination fail; explicit\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/gatipor\/robust-a-posteriori-error-estimates-for-reactiondiffusion-problems\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":932,"featured_media":1082,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1079","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/1079","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=1079"}],"version-history":[{"count":7,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/1079\/revisions"}],"predecessor-version":[{"id":1089,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/1079\/revisions\/1089"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media\/1082"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media?parent=1079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/categories?post=1079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/tags?post=1079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}