# FEM/FEA Documentation

## What is Finite Element Analysis?

### General definition

Finite Element Analysis (FEA) uses the finite element method (FEM) as a numerical method for solving problems of engineering and mathematical physics. Finite element methods are numerical methods for approximating the solutions of mathematical problems that are usually formulated so as to precisely state an idea of some aspect of physical reality. A finite element method is characterized by a variational formulation, a discretization strategy, one or more solution algorithms and post-processing procedures.

There are different types of finite element methods: AEM, generalized finite elment method, mixed finite element method, hp-FEM, XFEM, Meshfree methods or the strecthed grid method.

### Steps of a FEA

2. meshing
3. applying boundary conditions
4. run the simulation/solving
5. post processing/evaluating the results

### Problems which can be solved with FEA

FEA has a huge spectrum of problem solvings. The main purpose is in the solving of the mechanical and thermal behaviour of machine parts. But it is also used in civil engineering e.g. to calculate the bearing capacity of concrete structures.

Aeronautical, biomechanical, production and automotive industries commonly use integrated FEM in design and development of their products. But FEA can also be used in stochastic modelling for numerically solving probability models.

### Calculation – Partial Differential Equations

FEA allows static analysis, heat transfer simulation, fluid flow modelling and electromagnetic potential distributions. The finite element method formulation of these problems results in a system of algebraic equations. To solve a so modelled problem, the FEM baased solution is to subdivide a large problem into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEA then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

For the user the mathematical calculation aren’t that important and in most use cases it is enough to have a rough understanding of the functionality. For more details you can look at the wikipedia articles about Partial Differential Equations and FEM in general.