Analysis of a splitting method for incompressible inviscid rotational flow problems

摘要

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.