# Finite Element Method Questions and Answers – Approximation Errors

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

1. Which of the following is an error estimate method?
a) Priori method
b) Recurring method
c) Probing method
d) Primal method

Explanation: The priori method is one of the error estimate method. It helps decipher the order of convergence of a given finite element method. These estimate methods aim to give reasonable measures of efficiency of a given method by calculating how fast the error changes when the mesh size is reduced.

2. Which of the following is the role of an error estimate method?
a) Performing modal analysis
c) Making provision for non linear analysis
d) Making provision for linear analysis

Explanation: The error estimation method has two main functions. These help give a better idea of the actual error of a given finite element computation. Secondly, they are used for adaptive mesh refinement. In this refinement method, the posteriori method is used to indicate where the error is high, and thus use more mesh intervals in those locations.

3. Energy norm measures the errors both in their function values and their respective derivatives.
a) True
b) False

Explanation: The given statement is true. The energy method measures the error, both in its function values and error in the derivatives. This is considered as a drawback of the energy method. Computation of both the errors is not considered necessary at all times.

4. How many derivatives are expected in the Hermite Cubic method and piecewise linear method respectively?
a) One and three
b) Two and four
c) Three in both
d) Four and two

Explanation: The error estimates of the Hermite cubic method require that function u has four derivatives. Whereas, in the piecewise linear method, u is expected to have only two derivatives. Certain situations demand for two or lesser derivatives, and it only makes sense to us the piecewise linear method in such scenarios.

5. What is the first step of the mesh refinement process?
a) Galerkin method is made use of
b) Finite element approximation is performed for the exact solution
c) Finite element approximation is performed on a coarse grid
d) Rayleigh Ritz method is made use of

Explanation: Firstly, finite element approximation is performed on a coarse grid with minimal mesh points. The solution so obtained from this step is then used to determine where more mesh points should be placed. Following this, the model is recomputed to find out the error percentage resulting from the finer mesh.

6. Which of the following is an assumption of the posteriori method?
a) Order of differential equation and order of convergence are not related to one another
b) Order of differential equation < order of convergence of finite element method
c) Order of differential equation > order of convergence of finite element method
d) Order of differential equation = order of convergence of finite element method

Explanation: The posteriori method relies heavily on the assumption that the order of differential equation and order of convergence of the finite element method is the same. This is considered as a disadvantage as all problems solved using the Hermite cubic method do not satisfy the condition.

Sanfoundry Global Education & Learning Series – Finite Element Method.