Analysis of a splitting method for incompressible inviscid rotational flow problems

This paper is devoted to analyze a splitting method for solving incompressible inviscid rotational flows. The problem is first recast into the velocity-vorticity-pressure formulation by introducing the additional vorticity variable, and then split into three consecutive subsystems. For each subsystem, the L² least-squares finite element approach is applied to attain accurate numerical solutions. We show that for each time step this splitting least-squares approach exhibits an optimal rate of convergence in the H¹ norm for velocity and pressure, and a suboptimal rate in the L² norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates.