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SUMMARY:What are we computing with numerical methods for hyperbolic system
 s of conservation laws? - Professor Dr. Siddhartha Mishra\, Seminar for Ap
 plied Mathematics (SAM)\, D-MATH\, ETH Zurich\, Switzerland
DTSTART:20171018T150000Z
DTEND:20171018T160000Z
UID:TALK93712@talks.cam.ac.uk
CONTACT:June Rix
DESCRIPTION:Efficient numerical methods for approximating hyperbolic syste
 ms of conservation laws have been in existence for the past three decades.
  However\, rigorous convergence results to entropy solutions are only avai
 lable in the case of scalar conservation laws. We present numerical eviden
 ce that demonstrates the lack of convergence of state of art numerical met
 hods to entropy solutions of multi-dimensional systems. On the other hand\
 , an ensemble averaged version of these numerical methods is shown to conv
 erge to entropy measure-valued solutions. However\, these solutions are no
 t unique. We impose additional admissibility criteria by requiring propaga
 tion of information on all multi-point correlations. This results in the c
 oncept of statistical solutions or time-parametrized probability measures 
 on integrable functions\, as a solution framework. We derive sufficient co
 nditions for convergence of ensemble-averaged numerical methods to statist
 ical solutions and present numerical experiments illustrating these soluti
 ons. Open analytical and computational issues with this solution framework
  are also discussed.
LOCATION:MR9\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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