PUMA publications for /bibtexkey/journals/siamsc/BarthF16/leonkokkoliadishttps://puma.ub.uni-stuttgart.de/bibtexkey/journals/siamsc/BarthF16/leonkokkoliadisPUMA RSS feed for /bibtexkey/journals/siamsc/BarthF16/leonkokkoliadis2024-03-28T11:38:21+01:00Uncertainty Quantification for Hyperbolic Conservation Laws with Flux Coefficients Given by Spatiotemporal Random Fieldshttps://puma.ub.uni-stuttgart.de/bibtex/2ac028ba172702ffac95b7e930bc93e23/leonkokkoliadisleonkokkoliadis2020-03-05T13:48:02+01:002016 B07 sfbtrr161 <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Andrea Barth" itemprop="url" href="/person/1b1b958721ff8d51a5d30f7154c6f3414/author/0"><span itemprop="name">A. Barth</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Franz G. Fuchs" itemprop="url" href="/person/1b1b958721ff8d51a5d30f7154c6f3414/author/1"><span itemprop="name">F. Fuchs</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 Journal on Scientific Computing</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">38 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">A2209–A2231</span></em> </span>(<em><span>2016<meta content="2016" itemprop="datePublished"/></span></em>)</span>Thu Mar 05 13:48:02 CET 2020SIAM Journal on Scientific Computing4 A2209–A2231Uncertainty Quantification for Hyperbolic Conservation Laws with Flux Coefficients Given by Spatiotemporal Random Fields3820162016 B07 sfbtrr161 In this paper hyperbolic partial differential equations (PDEs) with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by correlated Gaussian random fields in space and Ornstein--Uhlenbeck processes in time. The resulting system of equations consists of a stochastic differential equation for each random parameter coupled to the hyperbolic conservation law. We define an appropriate solution concept in this setting and analyze errors and convergence of discretization methods. A novel discretization framework, based on Monte Carlo finite volume methods, is presented for the robust computation of moments of solutions to those random hyperbolic PDEs. We showcase the approach on two examples which appear in applications---the magnetic induction equation and linear acoustics---both with a spatiotemporal random background velocity field.