Trygve K. Karper
Institut de Mathématiques de Toulouse
Université Paul Sabatier

Convergence of a combined FEM-DG method for the compressible Navier-Stokes equations
In this talk, I will present a new numerical method for the approximation of viscous isentropic gas. The method approximates the density in the space of piecewise constants and the velocity in the Crouzeix-Raviart finite element space. The main result is that the method converges to a weak solution as discretization parameters go to zero. The proof of convergence is achieved by constructing a numerical analogy to the continuous existence theory of P.L. Lions and E. Feireisl.