Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations

Thierry Gallouët (1) , Raphaèle Herbin (1) , David Maltese (2) , Antonin Novotny (2)

1 I2M - Institut de Mathématiques de Marseille
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and space discretization. We use this methodology to derive an error estimate for a specific DG/finite element scheme for which the convergence was proved in [26].

Mots clés: Navier-Stokes equations; Compressible fluids; Finite volume methods AMS classification 35Q30; 65N12; 65N30; 76N15; 76N10; 76M10; 76M12; Relative energy; Error estimates; Finite element mlethods

Domaines: Mathématiques [math]

Thierry Gallouët, Raphaèle Herbin, David Maltese, Antonin Novotny. Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations. IMA Journal of Numerical Analysis, 2016, 36 (2), pp.543-592. ⟨10.1093/imanum/drv028⟩. ⟨hal-01108579⟩