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in Finite Element Method by (110k points)
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

1 Answer

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by (185k points)
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Best answer
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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