In FEM, which option is a negative aspect of the mixed formulation?

Involves a natural and direct formulation

Presence of zeros on matrix diagonals corresponding to pressure variable

Involves a natural and direct formulation

It is a velocity-pressure formulation

It is similar to the Lagrange multiplier method

In FEM, what is the characteristic of the problem with the functional Iv(v) representing governing equations of steady viscous incompressible flows?

It is subjected to constraint ( frac{ partial v_x}{ partial x}+ frac{ partial v_y}{ partial y} )=0

It can be reformulated as a constrained one, by using the penalty method

It cannot be reformulated as an unconstrained one, by using the penalty method

In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?

Lagrange multiplier formulation

Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?

Constraints are created by the elimination of velocity

Constrains are readily available

Constraints are created by the elimination of pressure

Constraints are created by the elimination of velocity

No constraints are dealt with in penalty formulation

Explore topic-wise MCQs in Finite Element Method.

This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Finite Element Method knowledge and support exam preparation. Choose a topic below to get started.

1.	In FEM, which option is a negative aspect of the mixed formulation?
A.	Presence of zeros on matrix diagonals corresponding to pressure variable
B.	Involves a natural and direct formulation
C.	It is a velocity-pressure formulation
D.	It is similar to the Lagrange multiplier method
Answer» B. Involves a natural and direct formulation

Discussion

2.	For the functional I_L(v, ) I_v(v)+ _{_c} G(v)dxdy, what is the necessary condition for I_L to have a stationary value?
A.	<sub>v<sub>x</sub></sub>I<sub>L</sub>+ <sub>v<sub>y</sub></sub>I<sub>L</sub>+ <sub> </sub>I<sub>L</sub>=0
B.	<sub>v<sub>x</sub></sub>I<sub>L</sub>- <sub>v<sub>y</sub></sub>I<sub>L</sub>- <sub> </sub>I<sub>L</sub>=0
C.	<sub>v<sub>x</sub></sub>I<sub>L</sub>- <sub>v<sub>y</sub></sub>I<sub>L</sub>+ <sub> </sub>I<sub>L</sub>=0
D.	<sub>v<sub>x</sub></sub>I<sub>L</sub>+ <sub>v<sub>y</sub></sub>I<sub>L</sub>- <sub> </sub>I<sub>L</sub>=0
Answer» B. <sub>v<sub>x</sub></sub>I<sub>L</sub>- <sub>v<sub>y</sub></sub>I<sub>L</sub>- <sub> </sub>I<sub>L</sub>=0

Discussion

3.	In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.
A.	True
B.	False
Answer» B. False

Discussion

4.	In FEM, what is the characteristic of the problem with the functional I_v(v) representing governing equations of steady viscous incompressible flows?
A.	It is subjected to constraint ( frac{ partial v_x}{ partial x}+ frac{ partial v_y}{ partial y} )=0
B.	It is an unconstrained problem
C.	It can be reformulated as a constrained one, by using the penalty method
D.	It cannot be reformulated as an unconstrained one, by using the penalty method
Answer» B. It is an unconstrained problem

Discussion

5.	For the functional I_v(v)= ( frac{1}{2} )B_v(v,v)-l(v), which option is equivalent to the equations governing steady flows of viscous incompressible fluids?
A.	Minimize l<sub>v</sub>
B.	Maximize l<sub>v</sub>
C.	Stationary l<sub>v</sub>
D.	Derivative of l<sub>v</sub>
Answer» B. Maximize l<sub>v</sub>

Discussion

6.	In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?
A.	Velocity-pressure formulation
B.	Penalty formulation
C.	Mixed formulation
D.	Lagrange multiplier formulation
Answer» C. Mixed formulation

Discussion

7.	Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?
A.	Constrains are readily available
B.	Constraints are created by the elimination of pressure
C.	Constraints are created by the elimination of velocity
D.	No constraints are dealt with in penalty formulation
Answer» C. Constraints are created by the elimination of velocity

Discussion

Explore topic-wise MCQs in Finite Element Method.

In FEM, which option is a negative aspect of the mixed formulation?

For the functional IL(v, ) Iv(v)+ c G(v)dxdy, what is the necessary condition for IL to have a stationary value?

In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.

In FEM, what is the characteristic of the problem with the functional Iv(v) representing governing equations of steady viscous incompressible flows?

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?

In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?

Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?

For the functional I_L(v, ) I_v(v)+ _{_c} G(v)dxdy, what is the necessary condition for I_L to have a stationary value?

In FEM, what is the characteristic of the problem with the functional I_v(v) representing governing equations of steady viscous incompressible flows?

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