Trygve Karper, Department for Mathematical Sciences, Norwegian University of Science and Technology, Norway In this talk, I will present a 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.

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