https://puma.ub.uni-stuttgart.de/tag/postprocessing%20continuousPUMA RSS feed for /tag/postprocessing%20continuous2026-04-12T15:52:33+02:00https://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> und <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, 2017https://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> und <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