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In finite element modeling, which formulation introduces constraints on variables and satisfies them in an approximate sense?

(a) Velocity-pressure formulation

(b) Penalty formulation

(c) Mixed formulation

(d) Lagrange multiplier formulation

I had been asked this question in semester exam.

My question is taken from Penalty topic in section Flows of Viscous Incompressible Fluids of Finite Element Method

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The correct choice is (b) Penalty formulation

Easy explanation: There are two different finite element models of momentum and continuity equations. The first one is a natural and direct formulation of momentum and continuity equations. The second model, penalty formulation, is based on the interpretation that the continuity equation is a new relationship among the velocity components, and it eliminates the pressure term leading to a constraint on the velocity components. The constraint is satisfied in a least-squares (i.e., approximate) sense.

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