# What's the Optimal Shape Function for Phase Field Simulations in FEM?

• feynman1
In summary, the best shape function/element for phase field simulation in finite element methods varies depending on the type of simulation being performed. Different shapes, such as triangular or quadrilateral elements, have been used in previous research for this type of analysis. If no benchmarks are available, it is recommended to try different element types and compare the results to determine the most suitable shape for the specific simulation.
feynman1
What's the best shape function/element in finite element methods for phase field simulation?

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feynman1 said:
What's the best shape function/element in finite element methods for phase field simulation?
What have you found so far? What shapes are typically used for which types of simulations?

https://www.researchgate.net/figure/Stress-results-of-the-FEM-simulation-of-brake-lever-after-optimization-Further_fig1_331572114

If you can't find any benchmarks for this type of analysis, it would be best to just try different element types and compare the results (i.e. do the benchmark yourself).

feynman1 and berkeman
Repeatedly starting threads with overly-broad questions and showing zero effort -- Temp Ban
berkeman said:
What have you found so far? What shapes are typically used for which types of simulations?

View attachment 298674
https://www.researchgate.net/figure/Stress-results-of-the-FEM-simulation-of-brake-lever-after-optimization-Further_fig1_331572114
little otherwise wouldn't have asked here

## 1. What is a shape function in finite element methods?

A shape function is a mathematical function used to approximate the behavior of a physical system in finite element analysis. It is used to represent the displacement or other physical quantities within an element in a finite element mesh.

## 2. How is the best shape function determined for phase field simulation?

The best shape function for phase field simulation is determined by considering the accuracy and efficiency of the method. This involves evaluating the convergence rate, stability, and computational cost of different shape functions.

## 3. What are the commonly used shape functions in finite element methods for phase field simulation?

The commonly used shape functions in finite element methods for phase field simulation include linear, quadratic, and cubic shape functions. These are also known as Lagrange shape functions and are used to approximate the solution within each element in the finite element mesh.

## 4. How does the choice of shape function affect the accuracy of phase field simulation?

The choice of shape function can significantly impact the accuracy of phase field simulation. Higher-order shape functions, such as quadratic or cubic, can improve the accuracy of the solution compared to linear shape functions. However, they also increase the computational cost of the simulation.

## 5. Can different shape functions be used within the same finite element mesh for phase field simulation?

Yes, different shape functions can be used within the same finite element mesh for phase field simulation. This is known as mixed or hybrid finite element methods and can provide a balance between accuracy and computational cost. However, it requires careful consideration and validation of the chosen shape functions.

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