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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

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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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