PUMA publications for /tag/galerkin,https://puma.ub.uni-stuttgart.de/tag/galerkin,PUMA RSS feed for /tag/galerkin,2024-03-28T21:35:35+01:00An adaptive wavelet space-time SUPG method for hyperbolic conservation
lawshttps://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mathematikmathematik2018-07-20T10:54:20+02:00(SUPG), Galerkin, Petrove-Galerkin adaptive conservation continuous discontinuous from:mhartmann hyperbolic ians laws, method, postprocessing spectral streamline upwind viscosity, vorlaeufig wavelet <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
laws332017(SUPG), Galerkin, Petrove-Galerkin adaptive conservation continuous discontinuous from:mhartmann hyperbolic ians laws, method, postprocessing spectral streamline upwind viscosity, vorlaeufig wavelet 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, 2017An adaptive wavelet space-time SUPG method for hyperbolic conservation
lawshttps://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mhartmannmhartmann2018-07-20T10:54:15+02:00(SUPG), Galerkin, Petrove-Galerkin adaptive conservation continuous discontinuous hyperbolic laws, method, postprocessing spectral streamline upwind viscosity, vorlaeufig wavelet <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 10:54:15 CEST 2018Numerical Methods for Partial Differential Equations62062-2089An adaptive wavelet space-time SUPG method for hyperbolic conservation
laws332017(SUPG), Galerkin, Petrove-Galerkin adaptive conservation continuous discontinuous hyperbolic laws, method, postprocessing spectral streamline upwind viscosity, vorlaeufig wavelet 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, 2017