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This paper discusses the numerical solution of the incompressible viscous flow by the fictitious domain method with distributed Lagrange multiplier. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. How to use the fictitious domain method applied to the Navier-Stokes equation is explained. The incompressible viscous flow is restricted by the distributed Lagrange multiplier method. Advantage of the fictitious domain method based on distributed Lagrange multiplier is investigated.

A Fictitious Domain Method with the Distributed Lagrange Multiplier for Incompressible Viscous Flow around Moving Particle