# Current Problems in Numerical Analysis

usually takes place each Friday, at 09:00 in IM, front building, third floor
Chair: Michal Křížek, Pavel Kůs, Jakub Šístek, Tomáš Vejchodský
Old web page with the seminar history: http://users.math.cas.cz/~okmma/

### On the convergence of a MAC scheme for the compressible Navier-Stokes system

##### Bangwei She
Institute of Mathematics of the CAS
Friday, 22. November 2019 - 9:00 to 10:00
We propose a finite difference Marker-And-Cell scheme for the compressible Navier-Stokes system. First, we show the stability and consistency of the numerical solution. Next, we prove the convergence of the numerical solution to the strong solution on the lifespan of the latter thanks to the dissipative measure-valued weak-strong uniqueness argument. Finally, employing the relative entropy functional, we show the convergence rate of the numerical solution.

### Spectral/hp Element Method and solver to Navier-Stokes-Fourier system with variable material properties

##### Jan Pech
Institute of Thermomechanics of the CAS
Friday, 13. December 2019 - 9:00 to 10:00

### Christmas lecture

##### Jan Brandts
University of Amsterdam
Friday, 20. December 2019 - 9:00 to 10:00

### Computing oscillatory solutions of the Euler system via $\mathcal{K}$-convergence

##### Bangwei She
Institute of Mathematics of the CAS
Friday, 17. January 2020 - 9:00 to 10:00
We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of $\mathcal{K}$-convergence adapted to sequences of parametrized measures. The convergence is strong  in space and time (a.e.~pointwise or in certain $L^q$ spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.