Analysis of a splitting method for incompressible inviscid rotational flow problems

Authors:
Chiung-Chiou Tsai;Suh-Yuh Yang
Affiliations:
Department of Civil Engineering, Nanya Institute of Technology, Jhongli City 32059, Taiwan;Department of Mathematics, National Central University, Jhongli City 32001, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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 L^2 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 H^1 norm for velocity and pressure, and a suboptimal rate in the L^2 norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates.