2017/09/04 by Javier de Frutos, Bosco Garcı́a-Archilla, de Frutos, Javier +5 · 1 citation
Engineering · #Stability and Controllability of Differential Equations #Fluid Dynamics and Turbulent Flows #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.1709.01011
This paper studies non inf-sup stable finite element approximations to the\nevolutionary Navier--Stokes equations. Several local projection stabilization\n(LPS) methods corresponding to different stabilization terms are analyzed,\nthereby separately studying the effects of the different stabilization terms.\nError estimates are derived in which the constants in the error bounds are\nindependent of inverse powers of the viscosity. For one of the methods, using\nvelocity and pressure finite elements of degree l, it will be proved that the\nvelocity error in L^\∞(0,T;L2(\Ω)) decays with rate l+1/2 in the\ncase that \ν\≤ h, with \ν being the dimensionless viscosity and h the\nmesh width. In the analysis of another method, it was observed that the\nconvective term can be bounded in an optimal way with the LPS stabilization of\nthe pressure gradient. Numerical studies confirm the analytical results.\n