(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, Samuele
A finite element error analysis of a local projection stabilization
(LPS) method for the time-dependent Navier-Stokes equations is presented. The
focus is on the highorder term-by-term stabilization method that has one
level, in the sense that it is defined on a single mesh, and in which the
projection-stabilized structure of standard LPS methods is replaced by an
interpolation-stabilized structure. The main contribution is on proving,
theoretically and numerically, the optimal convergence order of the arising
fully discrete scheme. In addition, the asymptotic energy balance is obtained
for slightly smooth flows. Numerical studies support the analytical results
and illustrate the potential of the method for the simulation of turbulent
ows. Smooth unsteady flows are simulated with optimal order of accuracy.
