# In FEM, what is the characteristic of the problem with the functional Iv(v) representing governing equations of steady viscous incompressible flows?

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In FEM, what is the characteristic of the problem with the functional Iv(v) representing governing equations of steady viscous incompressible flows?

(a) It is subjected to constraint  $\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}$=0

(b) It is an unconstrained problem

(c) It can be reformulated as a constrained one, by using the penalty method

(d) It cannot be reformulated as an unconstrained one, by using the penalty method

The question was posed to me during an interview for a job.

This intriguing question comes from Penalty topic in portion Flows of Viscous Incompressible Fluids of Finite Element Method

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Right option is (a) It is subjected to constraint  $\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}$=0

To explain: For the functional Iv(v), one can state that the equations governing steady flows of viscous incompressible fluids are equivalent to minimize Iv(v), subject to the constraint $\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}$=0. It is a constrained problem that can be reformulated as an unconstrained one by using the penalty method.

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