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

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• 作者：Trygve K. Karper
• 关键词：Primary ; 35Q30 ; 74S05 ; Secondary ; 65M12
• 刊名：Numerische Mathematik
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：125
• 期：3
• 页码：441-510
• 全文大小：605KB
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• 作者单位：Trygve K. Karper (1)
  
  1. Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, 20742, MD, USA
  
• ISSN：0945-3245

文摘

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.