{"ca15e451be40b14c5bec014bafe54360hermann":{"DOI":"10.1137/15M1027723","ISBN":"","ISSN":"1064-8275","URL":"","abstract":"In this paper hyperbolic partial differential equations (PDEs) with\n random coefficients are discussed. We consider the challenging problem\n of flux functions with coefficients modeled by spatiotemporal random\n fields. Those fields are given by correlated Gaussian random fields in\n space and Ornstein-Uhlenbeck processes in time. The resulting system of\n equations consists of a stochastic differential equation for each random\n parameter coupled to the hyperbolic conservation law. We de fine an\n appropriate solution concept in this setting and analyze errors and\n convergence of discretization methods. A novel discretization framework,\n based on Monte Carlo finite volume methods, is presented for the robust\n computation of moments of solutions to those random hyperbolic PDEs. We\n showcase the approach on two examples which appear in applications-the\n magnetic induction equation and linear acoustics both with a\n spatiotemporal random background velocity field.","annote":"","author":[{"family":"Barth","given":"Andrea"},{"family":"Fuchs","given":"Franz G."}],"citation-label":"ISI:000385283400013","collection-editor":[],"collection-title":"","container-author":[],"container-title":"SIAM JOURNAL ON SCIENTIFIC COMPUTING","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["{2016}"]],"literal":"{2016}"},"event-place":"3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA","id":"ca15e451be40b14c5bec014bafe54360hermann","interhash":"b1b958721ff8d51a5d30f7154c6f3414","intrahash":"ca15e451be40b14c5bec014bafe54360","issue":"4","issued":{"date-parts":[["{2016}"]],"literal":"{2016}"},"keyword":"Carlo Gaussian Monte Ornstein-Uhlenbeck differential equation; field; field} finite flux function; hyperbolic method; partial process; quantification; random spatiotemporal uncertainty volume {stochastic","misc":{"author-email":"{andrea.barth@mathematik.uni-stuttgart.de\n franzgeorgfuchs@gmail.com}","issn":"{1064-8275}","keywords-plus":"{FINITE-VOLUME METHODS; LINEAR TRANSPORT-EQUATION;\n DIFFERENTIAL-EQUATIONS; ADVECTION EQUATION; POLYNOMIAL CHAOS; SCHEMES;\n MULTIDIMENSIONS; SPEED}","funding-acknowledgement":"{German Research Foundation (DFG) as part of Cluster of Excellence in\n Simulation Technology at the University of Stuttgart {[}EXC 310/2]}","research-areas":"{Mathematics}","eissn":"{1095-7197}","number-of-cited-references":"{46}","affiliation":"{Barth, A (Reprint Author), Univ Stuttgart, SimTech, D-70569 Stuttgart, Germany.\n Barth, Andrea, Univ Stuttgart, SimTech, D-70569 Stuttgart, Germany.\n Fuchs, Franz G., SINTEF, N-0314 Oslo, Norway.}","web-of-science-categories":"{Mathematics, Applied}","language":"{English}","funding-text":"{SimTech, University of Stuttgart, 70569 Stuttgart, Germany\n (andrea.barth@mathematik.unistuttgart.de). This author's work was\n supported by the German Research Foundation (DFG) as part of the Cluster\n of Excellence in Simulation Technology (EXC 310/2) at the University of\n Stuttgart, and it is gratefully acknowledged.}","times-cited":"{0}","doi":"{10.1137/15M1027723}"},"note":"","number":"4","number-of-pages":"22","page":"A2209-A2231","page-first":"2209","publisher":"SIAM PUBLICATIONS","publisher-place":"3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA","status":"","title":"UNCERTAINTY QUANTIFICATION FOR HYPERBOLIC CONSERVATION LAWS WITH FLUX\n COEFFICIENTS GIVEN BY SPATIOTEMPORAL RANDOM FIELDS","type":"article-journal","username":"hermann","version":"","volume":"38"}}