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CATEGORIES:CMS Special Lectures
SUMMARY:What are we computing with numerical methods for h
yperbolic systems of conservation laws? - Professo
r Dr. Siddhartha Mishra\, Seminar for Applied Math
ematics (SAM)\, D-MATH\, ETH Zurich\, Switzerland
DTSTART;TZID=Europe/London:20171018T160000
DTEND;TZID=Europe/London:20171018T170000
UID:TALK93712AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/93712
DESCRIPTION:Efficient numerical methods for approximating hype
rbolic systems of conservation laws have been in e
xistence for the past three decades. However\, rig
orous convergence results to entropy solutions are
only available in the case of scalar conservation
laws. We present numerical evidence that demonstr
ates the lack of convergence of state of art numer
ical methods to entropy solutions of multi-dimensi
onal systems. On the other hand\, an ensemble aver
aged version of these numerical methods is shown t
o converge to entropy measure-valued solutions. Ho
wever\, these solutions are not unique. We impose
additional admissibility criteria by requiring pro
pagation of information on all multi-point correla
tions. This results in the concept of statistical
solutions or time-parametrized probability measure
s on integrable functions\, as a solution framewor
k. We derive sufficient conditions for convergence
of ensemble-averaged numerical methods to statist
ical solutions and present numerical experiments i
llustrating these solutions. Open analytical and c
omputational issues with this solution framework a
re also discussed.
LOCATION:MR9\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:June Rix
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