Finite difference and finite element methods – MCQs – EE

1. The finite difference method (FDM) is primarily used to:
(A) Solve algebraic equations only
(B) Solve differential equations approximately
(C) Solve optimization problems
(D) Solve integral equations exactly

2. In FDM, derivatives are replaced by:
(A) Integrals
(B) Difference quotients
(C) Polynomials
(D) Random numbers

3. Finite element method (FEM) divides the domain into:
(A) Nodes
(B) Elements
(C) Step sizes
(D) Intervals

4. In FEM, solution is approximated using:
(A) Exact function
(B) Interpolation functions
(C) Random values
(D) Polynomials only of degree one

5. FDM is more suitable for:
(A) Simple geometries
(B) Complex geometries
(C) Nonlinear systems only
(D) Stiff systems only

6. FEM is preferred for:
(A) Complex geometries and boundary conditions
(B) Simple one-dimensional problems
(C) Linear equations only
(D) Algebraic equations only

7. FDM accuracy improves by:
(A) Increasing the number of grid points
(B) Reducing the number of nodes
(C) Ignoring boundary conditions
(D) Using fewer elements

8. In FEM, the solution domain is divided into:
(A) Elements connected at nodes
(B) Independent points only
(C) Only boundaries
(D) Continuous region without discretization

9. Boundary conditions in FDM are applied:
(A) Only at the beginning
(B) At the edges of the grid
(C) Randomly in the domain
(D) Not required

10. The main steps in FEM include:
(A) Discretization, selection of shape functions, assembly, and solution
(B) Integration only
(C) Differentiation only
(D) Solving algebraic equations directly

11. FDM is easier to implement for:
(A) Uniform meshes
(B) Irregular meshes
(C) Complex geometries
(D) Nonlinear boundary conditions

12. FEM can handle which type of problems efficiently?
(A) Multi-dimensional and irregular domains
(B) Single point evaluation
(C) Only one-dimensional linear problems
(D) None of the above

13. In FDM, truncation error decreases with:
(A) Finer grid spacing
(B) Coarser grid spacing
(C) Ignoring derivatives
(D) Larger step size

14. In FEM, shape functions are used to:
(A) Approximate solution within an element
(B) Define boundary conditions only
(C) Integrate the system
(D) Reduce system size

15. Finite difference equations are derived from:
(A) Discretizing differential equations
(B) Solving algebraic equations
(C) Curve fitting
(D) Random sampling

16. FEM can be applied to:
(A) Structural problems
(B) Thermal analysis
(C) Electrical field problems
(D) All of the above

17. In FDM, central difference approximation is preferred because:
(A) It is more accurate than forward or backward difference
(B) It is faster
(C) It requires fewer points
(D) It ignores boundary conditions

18. The stiffness matrix in FEM represents:
(A) Relationship between nodal forces and displacements
(B) Only boundary conditions
(C) Only element shape
(D) Integration weights

19. In FDM, the grid spacing must be:
(A) Small enough to capture variation in solution
(B) Large enough to save computation
(C) Random
(D) Not important

20. FEM is more flexible than FDM for:
(A) Complex boundaries
(B) Simple one-dimensional problems
(C) Linear algebra only
(D) Euler’s method only

21. The main disadvantage of FDM is:
(A) Difficulty with complex geometries
(B) High computational cost
(C) Cannot solve differential equations
(D) Requires FEM implementation

22. In FEM, global equations are obtained by:
(A) Assembling element equations
(B) Solving element equations independently
(C) Ignoring boundary conditions
(D) Using difference quotients

23. FDM is primarily:
(A) Grid-based method
(B) Meshless method
(C) Polynomial fitting method
(D) Statistical method

24. In FEM, elements can be:
(A) One-dimensional, two-dimensional, or three-dimensional
(B) Only one-dimensional
(C) Only rectangular
(D) Only triangular

25. FDM equations lead to:
(A) Algebraic equations at each grid point
(B) Differential equations
(C) Random approximations
(D) Statistical models

26. FEM can be used to model:
(A) Mechanical structures
(B) Thermal systems
(C) Electromagnetic fields
(D) All of the above

27. Higher-order shape functions in FEM improve:
(A) Solution accuracy within an element
(B) Mesh generation
(C) Computation speed only
(D) Step size selection

28. The boundary conditions in FEM can be:
(A) Dirichlet or Neumann type
(B) Only Dirichlet
(C) Only Neumann
(D) Not required

29. FDM is generally easier to implement for:
(A) Regular geometries
(B) Irregular geometries
(C) Complex domains
(D) Multi-dimensional FEM

30. The main advantage of FEM over FDM is:
(A) Ability to handle complex geometries and boundary conditions
(B) Simpler implementation for uniform grids
(C) Less computational cost for simple problems
(D) Only works for one-dimensional problems