Discretization with h- and p-type solution methods
The last concept we are going to call attention to is the adaptive solution method. For this, it is appropriate to begin with a brief highlight of the key parameters of the Finite Element Method (FEM). Technically, to obtain accurate solutions via finite element simulations, there are two methods of control that can be imposed to approximate the response (that is, displacement, stress, strain, and so on) of a structure:
- Control of the mesh size: As the name implies, this control is associated with reducing the mesh size, which often means that as we reduce the mesh size, and hence use more elements, it is expected that the solution will converge to a finite accurate solution.
- Control of the order of polynomial: At a fundamental level, the finite element method is a brilliant combination of the theories of polynomial approximation of differential equations and matrix analysis. Hence, controlling the order of the...