FEM- and numerical analysis

Analytical calculations are based on exact formulas to solve problems. Using exact definitions and well-defined phenomena, exact solutions are found. We use analytical solutions as the first insight. A simple version of reality in which an analytical solution can be found gives us insight into the scale of the problem and a first indication of the situation.

Numerical methods such as FEM use numerical discretization to approach complex problems. The domain or geometry is divided into small parts, for which local solutions are defined. FEM is especially suitable for problems where the domain is complex and the relevant equations are difficult or impossible to solve with analytical methods. FEM is often used as a step after the analytical calculation to get a better approximation of the strength of a complex design, for example.