Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations
The authors consider the implicit Marker-And-Cell scheme (MAC scheme in short) for the compressible Navier-Stokes equations. Unconditional error estimates for a class of staggered schemes interesting from the point of view of mathematical simulations in two and three dimensional problems are derived. These are obtained using the discrete version of the relative energy method introduced on the continuous level in [\textit{E. Feireisl} et al., J. Math. Fluid Mech. 14, No. 4, 717--730 (2012; Zbl 1256.35054)], and involve the deep theoretical analysis of the continuous versions in combination with the numerical tools. This error estimate does not use stability hypotheses on the solution of the numerical scheme.
scientific article; zbMATH DE number 7017850
scientific article