# In the weak forms of the fluid flow model, since the weight functions are linearly dependent on each other, the sum of the three weak forms is the same as the three individual equations.

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In the weak forms of the fluid flow model, since the weight functions are linearly dependent on each other, the sum of the three weak forms is the same as the three individual equations.

(a) True

(b) False

This question was addressed to me during an interview.

The question is from Penalty in division Flows of Viscous Incompressible Fluids of Finite Element Method

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Correct choice is (b) False

Easy explanation: if x1, x2 and x3 represent three weak forms, then x1=ax2+bx3 is true only if the weight functions are linearly dependent. Since the weight functions are linearly independent of each other, the sum of the three weak forms is the same as the three individual equations i.e, the sum must be the expression x1+x2+x3 only.

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