PUMA publications for /user/hermann/field%7D%20uncertainty%20fluxhttps://puma.ub.uni-stuttgart.de/user/hermann/field%7D%20uncertainty%20fluxPUMA RSS feed for /user/hermann/field%7D%20uncertainty%20flux2024-03-28T20:59:27+01:00UNCERTAINTY QUANTIFICATION FOR HYPERBOLIC CONSERVATION LAWS WITH FLUX
COEFFICIENTS GIVEN BY SPATIOTEMPORAL RANDOM FIELDShttps://puma.ub.uni-stuttgart.de/bibtex/2ca15e451be40b14c5bec014bafe54360/hermannhermann2017-05-18T11:32:12+02:00Carlo Gaussian Monte Ornstein-Uhlenbeck differential equation; field; field} finite flux function; hyperbolic method; partial process; quantification; random spatiotemporal uncertainty volume {stochastic <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 May 18 11:32:12 CEST 2017{3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA}{SIAM JOURNAL ON SCIENTIFIC COMPUTING}{4}{A2209-A2231}{UNCERTAINTY QUANTIFICATION FOR HYPERBOLIC CONSERVATION LAWS WITH FLUX
COEFFICIENTS GIVEN BY SPATIOTEMPORAL RANDOM FIELDS}{Article}{38}{2016}Carlo Gaussian Monte Ornstein-Uhlenbeck differential equation; field; field} finite flux function; hyperbolic method; partial process; quantification; random spatiotemporal uncertainty volume {stochastic {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 de fine 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.}