{"id":226,"date":"2016-04-23T16:47:36","date_gmt":"2016-04-23T14:47:36","guid":{"rendered":"http:\/\/project.inria.fr\/gatipor\/?p=226"},"modified":"2021-12-02T22:03:39","modified_gmt":"2021-12-02T21:03:39","slug":"hp-adaptivity","status":"publish","type":"post","link":"https:\/\/project.inria.fr\/gatipor\/hp-adaptivity\/","title":{"rendered":"Potential and flux reconstructions a posteriori error estimates"},"content":{"rendered":"<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td><div id=\"attachment_140\" style=\"width: 910px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-1024x438.jpg\" alt=\"SIPG\" width=\"900\" height=\"385\" class=\"alignnone size-large wp-image-230\" srcset=\"https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-1024x438.jpg 1024w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-300x128.jpg 300w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-768x329.jpg 768w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-250x107.jpg 250w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG-150x64.jpg 150w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/SIPG.jpg 1547w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\"><strong>Asymptotic exactness<\/strong> for smooth Laplace solution, SIP discontinuous Galerkin method<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<td><div id=\"attachment_142\" style=\"width: 510px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-142\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3.jpg\" alt=\"hp_conv_E_3\" width=\"600\" height=\"575\" class=\"alignnone size-full wp-image-229\" srcset=\"https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3.jpg 600w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3-300x288.jpg 300w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3-157x150.jpg 157w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_3-150x144.jpg 150w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><p id=\"caption-attachment-142\" class=\"wp-caption-text\"><strong>Effectivity indices<\/strong> for hp-adaptivity with hanging nodes, IIP discontinuous Galerkin method<\/p><\/div><\/td>\n<td><div id=\"attachment_140\" style=\"width: 510px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-140\" src=\"http:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1.jpg\" alt=\"hp_conv_E_1\" width=\"600\" height=\"575\" class=\"alignnone size-full wp-image-228\" srcset=\"https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1.jpg 600w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1-300x288.jpg 300w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1-157x150.jpg 157w, https:\/\/project.inria.fr\/gatipor\/files\/2016\/07\/hp_conv_E_1-150x144.jpg 150w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><p id=\"caption-attachment-140\" class=\"wp-caption-text\"><strong>Exponential convergence<\/strong> for hp-adaptivity with hanging nodes, IIP discontinuous Galerkin method<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Main results<\/strong>:<\/p>\n<ul>\n<li>potential and equilibrated flux reconstruction estimates in a unified framework;<\/li>\n<li><strong>inhomogeneous<\/strong> Dirichlet and Neumann <strong>boundary conditions<\/strong>;<\/li>\n<li><strong>spatially varying polynomial degree<\/strong>;<\/li>\n<li><strong>mixed<\/strong> rectangular-triangular <strong>grids<\/strong>;<\/li>\n<li>combination with the <a href=\"http:\/\/rdcu.be\/vHnB\">H(div)-liftings paper<\/a>: <strong>robustness<\/strong> with respect to the <strong>number of hanging nodes<\/strong>;<\/li>\n<li><strong>asymptotic exactness<\/strong> observed for smooth solutions;<\/li>\n<li><em>hp<\/em>-adaptivity strategy numerically leading to <strong>exponential convergence<\/strong> even for singular solutions.<\/li>\n<\/ul>\n<p>Details: <a href=\"https:\/\/who.rocq.inria.fr\/Martin.Vohralik\/Files\/Pub_SISC_16.pdf\">paper<\/a> with V\u00edt Dolej\u0161\u00ed and Alexandre Ern and <a href=\"https:\/\/who.rocq.inria.fr\/Martin.Vohralik\/Files\/Exp_Linz_17.pdf\">presentation<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Main results: potential and equilibrated flux reconstruction estimates in a unified framework; inhomogeneous Dirichlet and Neumann boundary conditions; spatially varying polynomial degree; mixed rectangular-triangular grids; combination with the H(div)-liftings paper: robustness with respect to the number of hanging nodes; asymptotic exactness observed for smooth solutions; hp-adaptivity strategy numerically leading to\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/gatipor\/hp-adaptivity\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":932,"featured_media":229,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-226","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\/226","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=226"}],"version-history":[{"count":21,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/226\/revisions"}],"predecessor-version":[{"id":1053,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/posts\/226\/revisions\/1053"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media\/229"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/media?parent=226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/categories?post=226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/project.inria.fr\/gatipor\/wp-json\/wp\/v2\/tags?post=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}