Galerkin and subspace decomposition methods in space and time for the Navier–Stokes equations Original Research Article

The Galerkin method and the subspace decomposition method in space and time for the two-dimensional incompressible Navier–Stokes equations with the H2H2-initial data are considered. The subspace decomposition method consists of splitting the approximate solution as the sum of a low frequency component discretized by the small time step ΔtΔt and a high frequency one discretized by the large time step pΔtpΔt with p>1p>1. The H2H2-stability and L2L2-error analysis for the subspace decomposition method are obtained. Finally, some numerical tests to confirm the theoretical results are provided.