PUMA publications for /user/mathematik/Adaptivehttps://puma.ub.uni-stuttgart.de/user/mathematik/AdaptivePUMA RSS feed for /user/mathematik/Adaptive2024-03-29T10:40:50+01:00Distributed Newest Vertex Bisectionhttps://puma.ub.uni-stuttgart.de/bibtex/2cb88371212f23f2387c876de0c82ad50/mathematikmathematik2018-07-20T10:54:57+02:00from:mhartmann method Adaptive vorlaeufig ians <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Martin Alkämper" itemprop="url" href="/person/120fdeaf87d8fa0f67305283fd3e0234d/author/0"><span itemprop="name">M. Alkämper</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Robert Klöfkorn" itemprop="url" href="/person/120fdeaf87d8fa0f67305283fd3e0234d/author/1"><span itemprop="name">R. Klöfkorn</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Journal of Parallel and Distributed Computing</span>, </em> </span>(<em><span>2017<meta content="2017" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:57 CEST 2018Journal of Parallel and Distributed Computing1 - 11Distributed Newest Vertex Bisection1042017from:mhartmann method Adaptive vorlaeufig ians Distributed adaptive conforming refinement requires multiple iterations
of the serial refinement algorithm and global communication as the
refinement can be propagated over several processor boundaries. We
show bounds on the maximum number of iterations. The algorithm is
implemented within the open-source software package Dune-ALUGrid.Design of Finite Element Tools for Coupled Surface and Volume Mesheshttps://puma.ub.uni-stuttgart.de/bibtex/2d139b76a0d524aed7c15503f76b34fd4/mathematikmathematik2018-07-20T10:55:05+02:00from:mhartmann design software scientific Adaptive finite element software, methods, vorlaeufig ians <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Daniel Köster" itemprop="url" href="/person/1e9714704742940ccda41faa66c3346cc/author/0"><span itemprop="name">D. Köster</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Oliver Kriessl" itemprop="url" href="/person/1e9714704742940ccda41faa66c3346cc/author/1"><span itemprop="name">O. Kriessl</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/1e9714704742940ccda41faa66c3346cc/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">Numerical Mathematics: Theory, Methods and Applications</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">1 </span></span>(<span itemprop="issueNumber">3</span>):
<span itemprop="pagination">245-274</span></em> </span>(<em><span>2008<meta content="2008" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:55:05 CEST 2018Numerical Mathematics: Theory, Methods and Applications3245-274Design of Finite Element Tools for Coupled Surface and Volume Meshes12008from:mhartmann design software scientific Adaptive finite element software, methods, vorlaeufig ians Many problems with underlying variational structure involve a coupling
of volume with surface effects. A straight-forward approach in a
finite element discretization is to make use of the surface triangulation
that is naturally induced by the volume triangulation. In an adaptive
method one wants to facilitate "matching" local mesh modifications,
i.e., local refinement and/or coarsening, of volume and surface mesh
with standard tools such that the surface grid is always induced
by the volume grid. We describe the concepts behind this approach
for bisectional refinement and describe new tools incorporated in
the finite element toolbox ALBERTA. We also present several important
applications of the mesh coupling.Design and Convergence Analysis for an Adaptive Discretization of
the Heat Equationhttps://puma.ub.uni-stuttgart.de/bibtex/21237a0ffaf182fdd91641c941d3d4db1/mathematikmathematik2018-07-20T10:54:28+02:00parabolic problems, adaptive from:mhartmann elements, convergence finite analysis vorlaeufig ians <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Christian Kreuzer" itemprop="url" href="/person/14f9e70559b93e67305a10572434e4d6a/author/0"><span itemprop="name">C. Kreuzer</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Christian Möller" itemprop="url" href="/person/14f9e70559b93e67305a10572434e4d6a/author/1"><span itemprop="name">C. Möller</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Alfred Schmidt" itemprop="url" href="/person/14f9e70559b93e67305a10572434e4d6a/author/2"><span itemprop="name">A. Schmidt</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/14f9e70559b93e67305a10572434e4d6a/author/3"><span itemprop="name">K. Siebert</span></a></span></span>. </span><span class="additional-entrytype-information"><em>IMA J. Numer. Anal. doi:10.1093/imanum/drr026, </em>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)<em>Online First.</em></span>Fri Jul 20 10:54:28 CEST 2018IMA J. Numer. Anal. doi:10.1093/imanum/drr026IMA Journal of Numerical AnalysisOnline FirstDesign and Convergence Analysis for an Adaptive Discretization of
the Heat Equation2012parabolic problems, adaptive from:mhartmann elements, convergence finite analysis vorlaeufig ians We derive an algorithm for the adaptive approximation of solutions
to parabolic equations. It is based on adaptive finite elements in
space and the implicit Euler discretization in time with adaptive
time-step sizes. We prove that, given a positive tolerance for the
error, the adaptive algorithm reaches the final time with a space�time
error between continuous and discrete solution that is below the
given tolerance. Numerical experiments reveal a more than competitive
performance of our algorithm ASTFEM (adaptive space�time finite element
method).Convergence rates for adaptive finite elementshttps://puma.ub.uni-stuttgart.de/bibtex/2992b581f1e96812159406b320cdc362c/mathematikmathematik2018-07-20T10:54:31+02:00a estimator, equations posteriori adaptive from:mhartmann error refinement, vorlaeufig ians elliptic mesh <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Fernando D. Gaspoz" itemprop="url" href="/person/11e7a0334d6389891fae356da35076ece/author/0"><span itemprop="name">F. Gaspoz</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Pedro Morin" itemprop="url" href="/person/11e7a0334d6389891fae356da35076ece/author/1"><span itemprop="name">P. Morin</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 J. Numer. Anal.</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">29 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">917--936</span></em> </span>(<em><span>2009<meta content="2009" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:31 CEST 2018IMA J. Numer. Anal.4917--936Convergence rates for adaptive finite elements292009a estimator, equations posteriori adaptive from:mhartmann error refinement, vorlaeufig ians elliptic mesh Convergence of Adaptive Finite Element Methodshttps://puma.ub.uni-stuttgart.de/bibtex/26577a49d6be6cb03cd99ed10f5af9860/mathematikmathematik2018-07-20T10:54:26+02:00Hencky from:mhartmann elastoplasticity; Adaptive Convexity; FEM; vorlaeufig ians algorithm; elasticity; Convergence Linear <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Pedro Morin" itemprop="url" href="/person/182d27fed5937d15b2a4642665dea175f/author/0"><span itemprop="name">P. Morin</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Ricardo H. Nochetto" itemprop="url" href="/person/182d27fed5937d15b2a4642665dea175f/author/1"><span itemprop="name">R. Nochetto</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/182d27fed5937d15b2a4642665dea175f/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">SIAM Review</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">44 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">631-658</span></em> </span>(<em><span>2002<meta content="2002" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:26 CEST 2018SIAM Review4631-658Convergence of Adaptive Finite Element Methods442002Hencky from:mhartmann elastoplasticity; Adaptive Convexity; FEM; vorlaeufig ians algorithm; elasticity; Convergence Linear The a priori convergence of finite element methods is based on the
density property of the sequence of finite element spaces which essentially
assumes a quasi-uniform mesh-refining. The advantage is guaranteed
convergence for a large class of data and solutions; the disadvantage
is a global mesh refinement everywhere accompanied by large computational
costs. Adaptive finite element methods (AFEMs) automatically refine
exclusively wherever their refinement indication suggests to do so
and consequently leave out refinements at other locations. In other
words, the density property is violated on purpose and the a priori
convergence is not guaranteed automatically and, in fact, crucially
depends on algorithmic details. The advantage of AFEMs is a more
effective mesh in many practical examples accompanied by smaller
computational costs; the disadvantage is that the desirable convergence
property is not guaranteed a priori. Efficient error estimators can
justify a numerical approximation a posteriori and so achieve reliability.
But it is not theoretically justified from the start that the adaptive
mesh-refinement will generate an accurate solution at all. In order
to foster the development of a convergence theory and improved design
of AFEMs in computational engineering and sciences, this paper describes
a particular version of an AFEM and analyses convergence results
for three model problems in computational mechanics: linear elastic
material (A), nonlinear monotone elastic material (B), and Hencky
elastoplastic material (C). It establishes conditions sufficient
for error-reduction in (A), for energy-reduction in (B), and eventually
for strong convergence of the stress field in (C) in the presence
of small hardening.An adaptive wavelet space-time SUPG method for hyperbolic conservation
lawshttps://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mathematikmathematik2018-07-20T10:54:20+02:00Petrove-Galerkin postprocessing hyperbolic Galerkin, laws, spectral streamline upwind (SUPG), ians viscosity, adaptive from:mhartmann conservation continuous wavelet discontinuous vorlaeufig method, <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Hadi Minbashian" itemprop="url" href="/person/1c8972e3ab25e760174ed7741330758be/author/0"><span itemprop="name">H. Minbashian</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Hojatolah Adibi" itemprop="url" href="/person/1c8972e3ab25e760174ed7741330758be/author/1"><span itemprop="name">H. Adibi</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Mehdi Dehghan" itemprop="url" href="/person/1c8972e3ab25e760174ed7741330758be/author/2"><span itemprop="name">M. Dehghan</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Numerical Methods for Partial Differential Equations</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">33 </span></span>(<span itemprop="issueNumber">6</span>):
<span itemprop="pagination">2062-2089</span></em> </span>(<em><span>2017<meta content="2017" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:20 CEST 2018Numerical Methods for Partial Differential Equations62062-2089An adaptive wavelet space-time SUPG method for hyperbolic conservation
laws332017Petrove-Galerkin postprocessing hyperbolic Galerkin, laws, spectral streamline upwind (SUPG), ians viscosity, adaptive from:mhartmann conservation continuous wavelet discontinuous vorlaeufig method, This article concerns with incorporating wavelet bases into existing
streamline upwind Petrov-Galerkin (SUPG) methods for the numerical
solution of nonlinear hyperbolic conservation laws which are known
to develop shock solutions. Here, we utilize an SUPG formulation
using continuous Galerkin in space and discontinuous Galerkin in
time. The main motivation for such a combination is that these methods
have good stability properties thanks to adding diffusion in the
direction of streamlines. But they are more expensive than explicit
semidiscrete methods as they have to use space-time formulations.
Using wavelet bases we maintain the stability properties of SUPG
methods while we reduce the cost of these methods significantly through
natural adaptivity of wavelet expansions. In addition, wavelet bases
have a hierarchical structure. We use this property to numerically
investigate the hierarchical addition of an artificial diffusion
for further stabilization in spirit of spectral diffusion. Furthermore,
we add the hierarchical diffusion only in the vicinity of discontinuities
using the feature of wavelet bases in detection of location of discontinuities.
Also, we again use the last feature of the wavelet bases to perform
a postprocessing using a denosing technique based on a minimization
formulation to reduce Gibbs oscillations near discontinuities while
keeping other regions intact. Finally, we show the performance of
the proposed combination through some numerical examples including
Burgers�, transport, and wave equations as well as systems of shallow
water equations.� 2017 Wiley Periodicals, Inc. Numer Methods Partial
Differential Eq 33: 2062�2089, 2017ALBERT --- Software for Scientific Computations and Applicationshttps://puma.ub.uni-stuttgart.de/bibtex/28e5c4ef4cd89f8480d3267c8ac2ae0f5/mathematikmathematik2018-07-20T10:54:41+02:00from:mhartmann design software scientific Adaptive finite element software, methods, vorlaeufig ians <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Alfred Schmidt" itemprop="url" href="/person/1a5a8cd137415bf5bebd5688c3f8c4b73/author/0"><span itemprop="name">A. Schmidt</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Kunibert G. Siebert" itemprop="url" href="/person/1a5a8cd137415bf5bebd5688c3f8c4b73/author/1"><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">Acta Mathematica Universitatis Comenianae, New Ser.</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">70 </span></span>(<span itemprop="issueNumber">1</span>):
<span itemprop="pagination">105-122</span></em> </span>(<em><span>2001<meta content="2001" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:41 CEST 2018Acta Mathematica Universitatis Comenianae, New Ser.1105-122\textsf{ALBERT} --- {S}oftware for Scientific Computations and Applications702001from:mhartmann design software scientific Adaptive finite element software, methods, vorlaeufig ians Adaptive finite element methods are a modern, widely used tool which
make realistic computations feasible, even in three space dimensions.
We describe the basic ideas and ingredients of adaptive FEM and the
implementation of our toolbox \ALBERT. The design of \ALBERT is based
on the natural hierarchy of locally refined meshes and an abstract
concept of general finite element spaces. As a result, dimension
independent programming of applications is possible. Numerical results
from applications in two and three space dimensions demonstrate the
flexibility of \ALBERT.