Question

1. What is mesh convergence and how is it achieved in FEA in the absence of a known exact solution?

2. What are the four main sources of error in finite element model in order of least important to most important?

Answer 1

1. What is mesh convergence and how is it achieved in FEA in the absence of a known exact solution?

Mesh convergence is related to how small the elements need to be to ensure that the results of the finite element analysis are not affected by changing the size of the mesh.It is critical to first identify the quantity of interest. At least three points need to be considered, and as the mesh density increases, the quantity of interest starts to converge to a particular value. If two subsequent mesh refinements do not change the result substantially, then one can assume that the result has converged.

With regard to convergence, Burnett, 1987, offers the following summary.

1. If a model satisfies the completeness and continuity conditions (defined below), the energy of the Entire model will converge to the exact solution as the size of the elements are decreased.
2. In a well-posed problem (defined below), convergence of energy will also result in convergence of a particular local result in the model.
3. Once convergence of the particular result is graphically established, the error in the final result can be approximated by the error between final two solutions generated in the convergence study.

2. What are the four main sources of error in finite element model in order of least important to most important?

User Error - Incorrectly setting up the model due to inexperience.
Modeling errors due to simplifications (“We try to model the real world yet are not able to do it 100%.”)
Discretization errors that arise from the creation of the mesh.
Numerical errors of the solution of the FEA equations.