H- method and P- method in FEA

H- method and P- method

The three types of method are used to demonstrate the numerical convergence of the solution:

1. h - method
2. p - method
3. R - method

The h- and p- versions of the finite element method are different ways of adding degrees of freedom (DOF) to the model.

H-method

• The variable h is used to specify the step size in numeric integration.
• More accurate information is obtained by increasing the number of elements
• In order to increase the accuracy of the solution, more elements must be added. This means creating a finer mesh.
• The h-method improves results by using a finer mesh of the same type of element. This method refers to decreasing the characteristic length (h) of elements, dividing each existing element into two or more elements without changing the type of elements used.

P-method

• The p-method improves results by using the same mesh but increasing the displacement field accuracy in each element. 
• Large elements and complex shape functions are used in p-method problems.
• This method refers to increasing the degree of the highest complete polynomial (p) within an element without changing the number of elements used. 
•  Increasing the polynomial order increases the complexity of the shape function.
• The difference between the two methods lies in how these elements are treated. The h-method uses many simple elements, whereas the p-method uses few complex elements.

R -method

• It is a far less exploded method. It neither increases nor decreases the polynomial order not decrease the element character length.
• The mesh is refined simply by re-distributing the nodes in the domain such that the potential energy is reduced.