# How to Know Your Element Mesh Quality Is Good Enough?

When it comes to analyzing complex engineering systems, traditional methods simply won’t cut it. Finite element (FE) solutions have become essential for tackling intricate multiphysics problems. However, the quality of your FE mesh is crucial for obtaining accurate results.

## How can you determine if your mesh is good enough?

Although modern FE preprocessors have made it easier to create seemingly “good” meshes, it’s important to verify their quality for accurate analysis. A mesh that is “good enough” is one that produces results with an acceptable level of accuracy, assuming all other model inputs are accurate.

Mesh density is a key metric for accuracy (along with element type and shape). A high-density mesh will yield more accurate results, as long as there are no singularities present. However, overly dense meshes can lead to long run times and require excessive computer memory, especially for nonlinear and transient analyses that require multiple iterations.

Several methods exist for assessing mesh quality:

• Software mesh control features
• Mesh Metrics
• Convergence Analysis
• Test data or to theoretical values

Unfortunately, test data and theoretical results are often not available.  “Mesh Metrics” is one of the most useful features in determining the correct shape and size of the elements. You can find a range of criteria for quality check of your mesh, however, in this article, we will only explain, Aspect Ratio, Jacobian Ratio and Skewness.

### 1.Aspect Ratio

Aspect Ratio measures element quality, with a ratio of 1 indicating a perfectly shaped tetrahedral element. Higher ratios result in poorer element shapes.

### 2.Jacobian

Jacobian (or Jacobian Ratio) measures an element’s deviation from an ideal shape, with a range of -1.0 to 1.0. A value of 1.0 represents a perfectly shaped element.

### 3.Skewness

Skewness measures an element’s quality with respect to ideal element types. It determines how close a face or cell is to being equilateral or equi-angular. Skewness should fall between 0 and 0.5.

## Convergence Analysis

Convergence Analysis is the most accurate method for evaluating mesh quality. By refining the mesh until a critical result (such as maximum stress) converges, you can determine the optimal mesh density. Although this method can be time-consuming for complex models, tools like Convergence in Ansys automate the process by increasing mesh density and checking results between each step.

An example is shown below, where a 2D bracket model is constrained at its top end and subjected to a shear load at the edge on the lower right. This generates a peak stress in the fillet, as shown. The curve shows that as the mesh density increases, the peak stress in the fillet increases. Ultimately, increasing the mesh density further produces only minor increases in peak stress. In this case, an increase from 1134 elements per unit area to 4483 elements per unit area yields only a 1.5% increase in stress.

The problem with this method is that it requires multiple remeshing and re-solving operations. While this method is fine for simple models, it can be very time-consuming for complex models. However, in Ansys you can easily perform this operation automatically by using Convergence tool option.

Basically, the convergence tool increases the mesh density and checks the results between each step. You can easily see how your results change depending on the element quantity.

Good Luck!