https://puma.ub.uni-stuttgart.de/group/simtech/elementsPUMA RSS feed for /group/simtech/elements2026-04-23T03:49:20+02:00https://puma.ub.uni-stuttgart.de/bibtex/28fc4612e68ea6905b965ae8c7e92e656/mhartmannmhartmann2018-07-20T10:54:15+02:00adaptivity convergence elements finite density vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/1704190075ecceaf1b26aac9eeed999c5/author/0"><span itemprop="name">K. Siebert</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">IMA Journal of Numerical Analysis</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">31 </span></span>(<span itemprop="issueNumber">3</span>): <span itemprop="pagination">947-970</span></em> </span>(<em><span>2011<meta content="2011" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018IMA Journal of Numerical Analysis3947-970A Convergence Proof for Adaptive Finite Elements without Lower Bound312011adaptivity convergence elements finite density vorlaeufig We analyse the adaptive finite-element approximation to solutions of partial differential equations in variational formulation. Assuming well-posedness of the continuous problem and requiring only basic properties of the adaptive algorithm, we prove convergence of the sequence of discrete solutions to the true one. The proof is based on the ideas by Morin, Siebert and Veeser but replaces local efficiency of the estimator by a local density property of the adaptively generated finite-element spaces. As a result, estimators without a discrete lower bound are also included in our theory. The assumptions of the presented framework are fulfilled by a large class of important applications, estimators and adaptive strategies.https://puma.ub.uni-stuttgart.de/bibtex/205b87bcb8873845c63be5de24fb3d96a/mhartmannmhartmann2018-07-20T10:54:15+02:00equations;adaptive edge methods;Navier-Stokes investigation;numerical elements tones;experimental finite vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Andreas Bamberger" itemprop="url" href="/person/1fa7ad9b37dea72a7e6000abf9e4af3f9/author/0"><span itemprop="name">A. Bamberger</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Eberhard Bänsch" itemprop="url" href="/person/1fa7ad9b37dea72a7e6000abf9e4af3f9/author/1"><span itemprop="name">E. Bänsch</span></a></span>, </span> und <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/1fa7ad9b37dea72a7e6000abf9e4af3f9/author/2"><span itemprop="name">K. Siebert</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">ZAMM Journal of Applied Mathematics and Mechanics</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">84 </span></span>(<span itemprop="issueNumber">9</span>): <span itemprop="pagination">632-646</span></em> </span>(<em><span>2004<meta content="2004" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018ZAMM Journal of Applied Mathematics and Mechanics9632-646Experimental and numerical investigation of edge tones842004equations;adaptive edge methods;Navier-Stokes investigation;numerical elements tones;experimental finite vorlaeufig We study both, by experimental and numerical means the fluid dynamical phenomenon of edge tones. Of particular interest is the verification of scaling laws relating the frequency f to given quantities, namely d, the height of the jet, w, the stand�off distance and the velocity of the jet. We conclude that the Strouhal number Sd is related to the geometrical quantities through Sd = C � (d / w)n with n � 1, in contrast to some analytical treatments of the problem. The constant C of the experiment agrees within 13�15\% with the result of the numerical treatment. Only a weak dependence on the Reynolds number with respect to d is observed. In general, a very good agreement of the experimental and the numerical simulations is found.