In the variational problem of fluid flow, what is the correct matrix form of C in the bilinear form Bv(w,v)= e(Dw)TC(Dv)dx?

( begin{pmatrix}1&0&0 0&2&0 0&0&2 end{pmatrix} )

( begin{pmatrix}2&0&0 0&2&0 0&0&1 end{pmatrix} )

( begin{pmatrix}2&0&0 0&1&0 0&0&2 end{pmatrix} )

( begin{pmatrix}2&0&0 0&2&0 0&0&1 end{pmatrix} )

( begin{pmatrix}1&0&0 0&2&0 0&0&2 end{pmatrix} )

Which option is not correct concerning the bilinear term B(v,w) in the variational problem of the viscous fluid flow equation?

It contains the viscosity matrix

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

Only Bt(w,v)+Bv(w,v)-B p(w,P)=l(w)

Bt(w,v)+Bv(w,v)-B p(w,P)=l(w) and Bp(w3, v)=0

In finite element modeling, which formulation introduces constraints on variables and satisfies them in an approximate sense?

Lagrange multiplier formulation

In the weak forms of the fluid flow model, as the weight functions (w1, w2) are virtual variations of the velocity components(vx, vy ),respectively, which relation is satisfied by the weight functions?

( frac{ partial w2}{ partial x}+ frac{ partial w1}{ partial y} )=0

( frac{ partial w1}{ partial x}+ frac{ partial w2}{ partial y} )=0

( frac{ partial w2}{ partial x}+ frac{ partial w1}{ partial y} )=0

( frac{ partial w1}{ partial x}- frac{ partial w2}{ partial y} )=0

( frac{ partial w2}{ partial x}- frac{ partial w1}{ partial y} )=0

Which type of problem can be obtained by reformulating a problem with differential constraints by using the penalty method?

A problem with variable constraints

A problem with fixed constraints

A problem with structural constraints

10 + Mcqs in Penalty Finite Element Model 1 in Finite Element Method Page 1 McqOptions

1.	In the variational problem of fluid flow, what is the correct matrix form of C in the bilinear form B_v(w,v)= _{_e}(Dw)^TC(Dv)dx?
A.	( begin{pmatrix}2&0&0 0&2&0 0&0&1 end{pmatrix} )
B.	( begin{pmatrix}2&0&0 0&1&0 0&0&2 end{pmatrix} )
C.	( begin{pmatrix}2&0&0 0&2&0 0&0&1 end{pmatrix} )
D.	( begin{pmatrix}1&0&0 0&2&0 0&0&2 end{pmatrix} )
Answer» D. ( begin{pmatrix}1&0&0 0&2&0 0&0&2 end{pmatrix} )

Discussion

2.	Which option is not correct concerning the bilinear term B(v,w) in the variational problem of the viscous fluid flow equation?
A.	It is symmetric
B.	It contains the viscosity matrix
C.	B<sub>v</sub>(w,v)= B<sub>v</sub>(v,w)
D.	It is bilinear in both w and v
Answer» E.

Discussion

3.	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
Answer» C.

Discussion

4.	In the following variational problem of finding velocity components and pressure, which bilinear form includes time-derivative terms? B_t(w,v)+B_v(w,v)-B _p(w,P)=l(w); B_p(w₃, v)=0
A.	B<sub>t</sub>(w,v)
B.	B<sub>v</sub>(w,v)
C.	B <sub>p</sub>(w,P)
D.	B<sub>p</sub>(w<sub>3</sub>,v)
Answer» B. B<sub>v</sub>(w,v)

Discussion

5.	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 B<sub>t</sub>(w,v)+B<sub>v</sub>(w,v)-B <sub>p</sub>(w,P)=l(w)
B.	B<sub>t</sub>(w,v)+B<sub>v</sub>(w,v)-B <sub>p</sub>(w,P)=l(w) and B<sub>p</sub>(w<sub>3</sub>, v)=0
C.	Only B<sub>p</sub>(w<sub>3</sub>, v)=0
D.	B<sub>t</sub>(w,v)+B<sub>v</sub>(w,v)-B <sub>p</sub>(w,P)=0
Answer» C. Only B<sub>p</sub>(w<sub>3</sub>, v)=0

Discussion

6.	In finite element modeling, which formulation introduces constraints on variables and satisfies them in an approximate sense?
A.	Velocity-pressure formulation
B.	Penalty formulation
C.	Mixed formulation
D.	Lagrange multiplier formulation
Answer» C. Mixed formulation

Discussion

7.	In the weak forms of the fluid flow model, as the weight functions (w1, w2) are virtual variations of the velocity components(v_x, v_y ),respectively, which relation is satisfied by the weight functions?
A.	( frac{ partial w1}{ partial x}+ frac{ partial w2}{ partial y} )=0
B.	( frac{ partial w2}{ partial x}+ frac{ partial w1}{ partial y} )=0
C.	( frac{ partial w1}{ partial x}- frac{ partial w2}{ partial y} )=0
D.	( frac{ partial w2}{ partial x}- frac{ partial w1}{ partial y} )=0
Answer» B. ( frac{ partial w2}{ partial x}+ frac{ partial w1}{ partial y} )=0

Discussion

8.	In the penalty formulation of the fluid flow model, if the velocity field (v_x, v_y ) satisfies the continuity equation, then the weight functions (w1, w2) also satisfy the continuity equation.
A.	True
B.	False
Answer» C.

Discussion

9.	In the interest of the simple formulation of viscous flows, which case does not involve time derivative terms?
A.	Static case
B.	Transient case
C.	Unsteady case
D.	Non-periodic
Answer» B. Transient case

Discussion

10.	Which type of problem can be obtained by reformulating a problem with differential constraints by using the penalty method?
A.	A problem with no constraints
B.	A problem with variable constraints
C.	A problem with fixed constraints
D.	A problem with structural constraints
Answer» B. A problem with variable constraints

Discussion

Explore topic-wise MCQs in Finite Element Method.

In the variational problem of fluid flow, what is the correct matrix form of C in the bilinear form Bv(w,v)= e(Dw)TC(Dv)dx?

Which option is not correct concerning the bilinear term B(v,w) in the variational problem of the viscous fluid flow equation?

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.

In the following variational problem of finding velocity components and pressure, which bilinear form includes time-derivative terms?Bt(w,v)+Bv(w,v)-B p(w,P)=l(w); Bp(w3, v)=0

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

In finite element modeling, which formulation introduces constraints on variables and satisfies them in an approximate sense?

In the weak forms of the fluid flow model, as the weight functions (w1, w2) are virtual variations of the velocity components(vx, vy ),respectively, which relation is satisfied by the weight functions?

In the penalty formulation of the fluid flow model, if the velocity field (vx, vy ) satisfies the continuity equation, then the weight functions (w1, w2) also satisfy the continuity equation.

In the interest of the simple formulation of viscous flows, which case does not involve time derivative terms?

Which type of problem can be obtained by reformulating a problem with differential constraints by using the penalty method?

In the variational problem of fluid flow, what is the correct matrix form of C in the bilinear form B_v(w,v)= _{_e}(Dw)^TC(Dv)dx?

In the following variational problem of finding velocity components and pressure, which bilinear form includes time-derivative terms?
B_t(w,v)+B_v(w,v)-B _p(w,P)=l(w); B_p(w₃, v)=0

In the weak forms of the fluid flow model, as the weight functions (w1, w2) are virtual variations of the velocity components(v_x, v_y ),respectively, which relation is satisfied by the weight functions?

In the penalty formulation of the fluid flow model, if the velocity field (v_x, v_y ) satisfies the continuity equation, then the weight functions (w1, w2) also satisfy the continuity equation.