The FEM then approximates a solution by minimizing an associated error function via the calculus of variations. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The method approximates the unknown function over the domain.

The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.

The finite element method ( FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling.

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