A Dynamic Penalty or Projection Method for Incompressible Fluids
Journal of Scientific Computing
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Projection methods are an efficient tool to approximate strong solutions of the incompressible Navier-Stokes equations. As a major deficiency, these methods often suffer from reduced accuracy for pressure iterates caused by nonphysical boundary data, going along with suboptimal error estimates for pressure iterates. We verify a rigorous bound for arising boundary layers in Chorin's scheme under realistic regularity assumptions. In a second step, the new Chorin-Penalty method is proposed, where optimal rate of convergence for pressure iterates is shown.