{"id":1071,"date":"2021-12-02T18:42:52","date_gmt":"2021-12-02T17:42:52","guid":{"rendered":"http:\/\/project.inria.fr\/gatipor\/?p=1071"},"modified":"2021-12-02T23:46:34","modified_gmt":"2021-12-02T22:46:34","slug":"a-posteriori-error-estimates-for-linear-advection-problems","status":"publish","type":"post","link":"https:\/\/project.inria.fr\/gatipor\/a-posteriori-error-estimates-for-linear-advection-problems\/","title":{"rendered":"Robust a posteriori error estimates for linear advection problems"},"content":{"rendered":"<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td>\n<p><div id=\"attachment_140\" style=\"width: 910px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_adv.png\"><img decoding=\"async\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2021\/12\/a_post_adv.png\" alt=\"advection\" width=\"900\" class=\"alignnone size-large wp-image-452\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\">Errors (left) and estimators (right), discontinuous solution with aligned triangulation<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Main results<\/strong>:<\/p>\n<ul>\n<li> steady linear advection equation;<\/li>\n<li> rigorous results in 1D, heuristic extensions to mD;<\/li>\n<li> <strong>a posteriori error estimates<\/strong>:\n<ul>\n<li> <strong>guaranteed<\/strong> upper bound in the <em>L<sup>2<\/sup><\/em> norm;<\/li>\n<li> <strong>local efficiency<\/strong>;<\/li>\n<li> <strong>robustness<\/strong> with respect to <strong>advection dominance<\/strong> and <strong>polynomial degree<\/strong>;<\/li>\n<\/ul>\n<\/li>\n<li> numerically asymptotic exactness.<\/li>\n<\/ul>\n<p>Details: <a href=\"https:\/\/www.esaim-m2an.org\/articles\/m2an\/abs\/2021\/01\/m2an190084\/m2an190084.html\">paper<\/a> (<a href=\"https:\/\/hal.inria.fr\/hal-02105418\">preprint<\/a>) with Alexandre Ern and Mohammad Zakerzadeh.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Main results: steady linear advection equation; rigorous results in 1D, heuristic extensions to mD; a posteriori error estimates: guaranteed upper bound in the L2 norm; local efficiency; robustness with respect to advection dominance and polynomial degree; numerically asymptotic exactness. Details: paper (preprint) with Alexandre Ern and Mohammad Zakerzadeh.<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/gatipor\/a-posteriori-error-estimates-for-linear-advection-problems\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":932,"featured_media":1070,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1071","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\/1071","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=1071"}],"version-history":[{"count":3,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/1071\/revisions"}],"predecessor-version":[{"id":1074,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/1071\/revisions\/1074"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media\/1070"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media?parent=1071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/categories?post=1071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/tags?post=1071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}