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Optimal error estimate for a mixed finite element method for compressible Navier–Stokes system. (English) Zbl 1061.76031

Summary: We consider a linearized stationary compressible viscous Navier-Stokes system. A mixed finite element method is applied, and the unique existence of solution is established by the inf-sup condition. The convection terms, especially in the continuity equation, were thought of causing non-optimal order convergence, but in this paper error estimates of optimal order are derived by implementing the lowest-order Raviart-Thomas elements. The error estimates for normal and tangential components of velocity are also optimal on the interfaces of interior triangles. It turns out that the non-symmetric discrete system can be reformulated into a symmetric form.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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