# CIRP Encyclopedia of Production Engineering

2014 Edition
| Editors: The International Academy for Production Engineering, Luc Laperrière, Gunther Reinhart

# Finite Element Method

• A. Erman Tekkaya
• Celal Soyarslan
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-20617-7_16699

## Definition

A numerical method used to approximate the solution of boundary- and initial-value problems characterized by partial differential equations.

## Theory

The finite element method is a systematic procedure of approximating continuous functions as discrete models. This discretization involves finite number of points and subdomains in the problem’s domain. The values of the given function are held at the points, so-called nodes. The non-overlapping subdomains, so-called finite elements, are connected together at nodes on their boundaries and hold piecewise and local approximations of the function, which are uniquely defined in terms of values held at their nodes. The collection of discretized elements and nodes is called the mesh and the process of its construction is called meshing. A typical finite element partition of a two-dimensional domain with triangular finite elements is given in Fig. 1.
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