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

2015/04/11 by Thierry Gallouët, Gallouet, Thierry, Raphaèle Herbin +5 · 1 citation
Engineering · Mathematics · #35Q30 #65N12 #65N30 #76M10 #76M12 #76N10 #76N15 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1504.02890

openalex publication_date 2015/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present here a general method based on the investigation of the relative\nenergy of the system, that provides an unconditional error estimate for the\napproximate solution of the barotropic Navier Stokes equations obtained by time\nand space discretization. We use this methodology to derive an error estimate\nfor a specific DG/finite element scheme for which the convergence was proved in\n[27]. This is an extended version of the paper submitted to IMAJNA.\n

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• Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations

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