# In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?

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In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?

(a) Velocity-pressure formulation

(b) Penalty formulation

(c) Mixed formulation

(d) Lagrange multiplier formulation

I got this question by my school teacher while I was bunking the class.

My doubt stems from Penalty topic in portion Flows of Viscous Incompressible Fluids of Finite Element Method

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Correct answer 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. It is known as the velocity-pressure formulation or mixed formulation. Lagrange multiplier formulation is similar to the velocity-pressure formulation. The penalty formulation is not natural and direct.

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