Dear Merwan Behar

I recommend the Spectral Finite Element Method.

If you want to do in depth analysis by customising various variables such element size, material properties, damping, and method analysis etc, then it is better to use APDL. On the other hand if you want to focus only on the results without knowing about details of analyses parameters,you can opt for Workbench

Galerkin finite element method is fairly accurate and widely utilized.

There are at least two tricks to make even the Galerkin method even more efficient computationally.

1) For higher order elements (quadratic, cubic, etc...), you can write the degrees of freedom at the interior of elements in terms of the degrees of freedom at the skeleton of the mesh (this is called static condensation of interior-element degrees of freedom). This reduces the size of the main linear system you have to solve, although it requires a post processing step to recover the interior-element degrees of freedom values (could be done in parallel)

2) Define the nodes of your polynomial space to be the same nodes of the quadrature points. Usually, the nodes of a polynomial space in finite elements are equally spaced in a given direction. This is the classical approach and almost no one cares to do differently. However, in terms of approximation, you could very well choose different nodes. If you happen to choose them to be the quadrature points, then a lot of computations can be save when applying the quadrature rule. The resulting Galerkin method is even equivalent to collocation-type Runge-Kutta methods.

There is no such thing as most efficient method. All methods such as point collocation methods or variational parameters are worth solving and trying. Its just that we need to understand what type of problem we are solving for.