Publications 2018

Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions
E. Feireisl, M. Lukacova-Medvidova
Found. Comput. Math. 18 , 703–730 (2018);
doi: DOI: 10.1007/s10208-017-9351-2

↓ Show Abstract↑ Hide Abstract We study convergence of a mixed finite element-finite volume numerical scheme for the isentropic Navier-Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solutions of the limit system. In particular, using the recently established weak{strong uniqueness principle in the class of dissipative measure-valued solutions we show that the numerical solutions converge strongly to a strong solutions of the limit system as long as the latter exists.

Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
E. Feireisl, M. Lukacova-Medvidova, S. Necasova, A. Novotny, B. She
SIAM Multiscale Model. Simul. 16 (1), 150–183 (2018);
URL: https://epubs.siam.org/doi/10.1137/16M1094233

↓ Show Abstract↑ Hide Abstract We study the convergence of numerical solutions of the compressible Navier-Stokes system to its incompressible limit. The numerical solution is obtained by a combined finite element-finite volume method based on the linear Crouzeix-Raviart finite element for the velocity and piecewise constant approximation for the density. The convective terms are approximated using upwinding. The distance between a numerical solution of the compressible problem and the strong solution of the incompressible Navier-Stokes equations is measured by means of a relative energy functional. For barotropic pressure exponent larger than 3/2 and for well-prepared initial data we obtain uniform convergence of order. Extensive numerical simulations confirm that the numerical solution of the compressible problem converges to the solution of the incompressible Navier-Stokes equations as the discretization parameters and the Mach number tend to zero.

Unfolding dynamics of small peptides biased by constant mechanical forces
Fabian Knoch, Thomas Speck
Molecular Systems Design & Engineering, (2018);
doi:10.1039/c7me00080d