What are we computing with numerical methods for hyperbolic systems of conservation laws ?

Add to your list(s) Download to your calendar using vCal

• Professor Dr. Siddhartha Mishra, Seminar for Applied Mathematics (SAM), D-MATH, ETH Zurich, Switzerland
• Wednesday 06 September 2017, 15:00-16:00
• MR3, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact June Rix.

This talk has been canceled/deleted

Efficient numerical methods for approximating hyperbolic systems of conservation laws have been in existence for the past three decades. However, rigorous convergence results to entropy solutions are only available in the case of scalar conservation laws. We present numerical evidence that demonstrates the lack of convergence of state of art numerical methods to entropy solutions of multi-dimensional systems. On the other hand, an ensemble averaged version of these numerical methods is shown to converge to entropy measure-valued solutions. However, these solutions are not unique. We impose additional admissibility criteria by requiring propagation of information on all multi-point correlations. This results in the concept of statistical solutions or time-parametrized probability measures on integrable functions, as a solution framework. We derive sufficient conditions for convergence of ensemble-averaged numerical methods to statistical solutions and present numerical experiments illustrating these solutions. Open analytical and computational issues with this solution framework are also discussed.

This talk is part of the CMS Special Lectures series.

This talk is included in these lists:

This talk is not included in any other list

Note that ex-directory lists are not shown.