This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Various Measures of Finite Element Errors”.

1. For any conventional problem, the finite element error is considered to be proportional to the mth derivative of that point alone.

a) True

b) False

View Answer

Explanation: The given statement is false. For any conventional problem, the finite element error is considered to be proportional to the product of m

^{th}derivative at that point and the element size h raised to the p

^{th}power. It is mathematically represented as –

e(x) = µ h

^{p}d

^{m}u(x)/dxm

where µ = constant of proportionality

2. What role does the value of gradient play in error analysis of finite element method?

a) If gradient is high, the mesh size should be less

b) If gradient is high, the mesh size should be more

c) If gradient is high, the mesh size should be constant

d) If gradient is high, the mesh size should be variable

View Answer

Explanation: Gradient refers to the value of the m

^{th}derivative. If the value of gradient is expected to be high, then the element/mesh size should be small. Whereas, if the value of gradient is expected to be less, then the element/mesh size should be big. This helps reduce costs and computation time incurred.

3. How is discretization error related to the polynomial form in finite element method?

a) It is extrinsic in nature

b) It is intrinsic in nature

c) It is concentric in nature

d) It is neutral in nature

View Answer

Explanation: The discretization error is intrinsic to the polynomial form of the finite element method. Convergence is said to be attained only if C and n+1

^{th}are bounded to one another. This error ceases to zero as the element size diminishes.

4. What do the h and p method correspond to?

a) Classical approaches to finite element method

b) Variational approaches to finite element method

c) Error identification techniques

d) Error reduction techniques

View Answer

Explanation: Both the h and p method correspond to error reduction techniques. Reduction of error by mesh refinement method corresponds to the h method. Whereas, reduction of error by increasing the approximation order while keeping sizes constant corresponds to the p method.

5. Which of the following is an error that is found in geometry approximation?

a) Perfect mesh analysis

b) Geometry approximation of the exact order

c) Geometry approximation of a lower order

d) Perfect constraint application

View Answer

Explanation: Errors in geometry approximation occur usually due to two reasons. It could be either due to geometry approximation of a lower order, or ignorance of the exact analytical form of the required geometry. Usage of isoparametric elements is considered a good error rectification technique for such errors.

6. Which of the following defines a truncating error?

a) Essential information of correct solution being lost due to truncation

b) Essential information of correct solution being found due to truncation

c) No such error exists

d) Every error occurring in the finite element method is a truncating error

View Answer

Explanation: This is a type of error that arises due to the internal conflicts of the computer/machine used for computation. When a system allocates a certain number of digits for data storage, only values corresponding to this number are stored. The other values are truncated, leading to loss of solution.

7. Which of the following defines a round off error?

a) Adjustment automatically performed by human

b) Adjustment automatically performed by computer

c) Adjustment manually performed by computer

d) Adjustment not performed by computer

View Answer

Explanation: Round off error corresponds to the adjustment automatically performed by a computer on the last digit of every value during computations. This is considered of very little importance when compared to a truncating error. However, defining of parameters and other values of importance should be done keeping maximum number of digits in mind.

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