Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
This provides a rigorous error analysis framework for numerical schemes in computational fluid dynamics, but the result is incremental as it extends existing convergence results to error estimates.
The authors develop a general method using relative energy to obtain unconditional error estimates for numerical approximations of the compressible barotropic Navier-Stokes equations, and apply it to a specific DG/finite element scheme, proving an error estimate for a scheme whose convergence was previously established.
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 [27]. This is an extended version of the paper submitted to IMAJNA.