Galerkin and subspace decomposition methods in space and time for the Navier-Stokes equations

The Galerkin method and the subspace decomposition method in space and time for the two-dimensional incompressible Navier-Stokes equations with the H²-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 Δt and a high frequency one discretized by the large time step pΔt with p>1. The H²-stability and L²-error analysis for the subspace decomposition method are obtained. Finally, some numerical tests to confirm the theoretical results are provided.