Steps in FEM: An Overview

Figure 1 is a flowchart illustrating the FEM process for a linear static problem (the concept is similar to more complex problems):

Figure 1: A finite element method process for solving linear static problems (Click to enlarge)

Brief explaination of the different stages in Figure 1:

1. Boundary Description - Create a control volume and fully describe the boundary value problem 
2. Principle of Virtual Work - Derive a weak formulation of the differential equations using a virtual function
3. Meshing - Discretise continuum into finite number of elements and define element type and connectivity using shape functions 
4. FE Equation (General) - obtain the general FE equation by applying virtual work equations to the mesh 
5. Matrix Assembly - Calculate local stiffnesses (k) and forces (f (body and surface)) and assemble into global stiffness (K) and force (f (nodal)) matrices 
6. FE Equation (Problem Specific) - An FE equation specific to the problem is obtained upon assembling K and f(nodal). For the classic linear elastic problem, this looks like KU = f. 
7. Matrix Inversion - involves a series of steps to manipulate and invert matrix 
8. Obtain U - the eventual aim of FEM is to obtain displacement (U), which contains information about all nodal displacements. Once U is computed from matrix inversion, we can calculate strains from U, stresses from strains and so on.

FAQ - What's the difference between boundary and displacement boundary conditions?

Also read
Steps in FEA
FEA vs. FEM