# For the functional Iv(v)=$\frac{1}{2}$Bv(v,v)-l(v), which option is equivalent to the equations governing steady flows of viscous incompressible fluids?

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For the functional Iv(v)=$\frac{1}{2}$Bv(v,v)-l(v), which option is equivalent to the equations governing steady flows of viscous incompressible fluids?

(a) Minimize   lv

(b) Maximize  lv

(c) Stationary   lv

(d) Derivative of     lv

The question was asked during an online exam.

My question is based upon Penalty topic in portion Flows of Viscous Incompressible Fluids of Finite Element Method

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The correct choice is (a) Minimize   lv

Best explanation: For the quadratic functional given by the equation Iv(v)=$\frac{1}{2}$Bv(v,v)-l(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 of finding velocity.

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