As I have learned for now, there are several families of Polynomial-type Basis functions (Lagrange, Serendipity, Hermite, ...). My question is beside the order of the elements which affects the order of the Polynomial of the basis functions (Linear, Quadratic, Cubic).
How it comes that in some problems we use Lagrange family and others we use other families?
Does the choice of the Polynomial family depend on the problem we are facing (Linear/Nonlinear, extension/pressure, bending/torsion)?
Supposing that we have chosen a certain geometry of elements (Tetra or Hexa) how can the choice of the family of the basis functions affect the accuracy of the results for the same types of element and same mesh?
Does anyone know about something about this issue?