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arXiv · 1206.4368

A convergent FEM-DG method for the compressible Navier-Stokes equations

Trygve K. Karper
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Abstract

This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on piecewise constants and a basic upwind flux. For the momentum equation, the method is a new combined discontinuous Galerkin and finite element method approximating the velocity in the Crouzeix-Raviart finite element space. While the diffusion operator is discretized in a standard fashion, the convection and time-derivative are discretized using discontinuous Galerkin on the element average velocity and a Lax-Friedrich type flux. Our main result is convergence of the method to a global weak solution as discretization parameters go to zero. The convergence analysis constitutes a numerical version of the existence analysis of Lions and Feireisl.

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Trygve K. Karper. 2012-06-20. A convergent FEM-DG method for the compressible Navier-Stokes equations. https://arxiv.org/abs/1206.4368

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