# In the formulation of the finite element model, which option is the complete restated form of the weak forms of viscous fluids flow equations?

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In the formulation of the finite element model, which option is the complete restated form of the weak forms of viscous fluids flow equations?

(a) Only Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w)

(b) Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w) and –Bp(w3, v)=0

(c) Only –Bp(w3, v)=0

(d) Bt(w,v)+Bv(w,v)-B̅p(w,P)=0

The question was asked at a job interview.

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

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Right answer is (b) Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w) and –Bp(w3, v)=0

Best explanation: The problem described by weak forms of viscous fluids flow equations can be restated as a variational problem of finding (vx, vy, P) such that  Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w) and –Bp(w3, v)=0 holds for all weight functions (w1, w2, w3) and t>0. Here, we have used the notation w=$\begin{Bmatrix}w_1\\w_2\end{Bmatrix},$v=$\begin{Bmatrix}v_x\\v_y\end{Bmatrix},$ f=$\begin{Bmatrix}f_x\\f_y\end{Bmatrix}$ and t=$\begin{Bmatrix}t_x\\t_y\end{Bmatrix}$.

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