The finite element method (FEM), also referred to as finite element analysis (FEA) is a computational technique used to obtain approximate solutions of boundary value problems in engineering.
A boundary value problem is a mathematical problem in which one or more dependent variables must satisfy a differential equations everywhere within a known domain of the independent variables and satisfy specific conditions on the boundary of the domain.
Boundary value problems are also known as field problems. The field is the domain of interest and the most often represent a physical structure. The field variables are the dependent variables of interest governed by the differential equations. The boundary conditions are the specified values of the field variables (or related variables such as derivatives) on the boundaries of the field. Depending on the type of physical problem being analyzed, the field variables may include displacement, temperature, heat flux, fluid velocity etc.