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A Discontinuous Galerkin Method for Convection-Dominated Compressible Viscous Navier-Stokes Equations with an Inflow Boundary Condition

Jae Ryong Kweon
SIAM Journal on Numerical Analysis
Vol. 38, No. 3 (2001), pp. 699-717
Stable URL: http://www.jstor.org/stable/3061983
Page Count: 19
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A Discontinuous Galerkin Method for Convection-Dominated Compressible Viscous Navier-Stokes Equations with an Inflow Boundary Condition
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Abstract

A linearized steady-state compressible viscous Navier-Stokes system with an inflow boundary condition is considered. A discontinuous Galerkin method for this system is formulated with convection-dominance and O(h) viscous functions where h is the mesh size in a given triangulation. The resulting finite element method is explicit and valid for all polynomials of degree ≥ 1. We show a Lp-stability and derive error estimates for velocity and pressure, respectively. In particular, the compressibility number κ := ρ′/ρ is regarded as essential in showing our stability results.

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