CIRP Encyclopedia of Production Engineering

2019 Edition
| Editors: Sami Chatti, Luc Laperrière, Gunther Reinhart, Tullio Tolio

Finite Element Method

  • A. Erman TekkayaEmail author
  • Celal Soyarslan
Reference work entry



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


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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Authors and Affiliations

  1. 1.Institute of Forming Technology and Lightweight ConstructionTechnische Universität DortmundDortmundGermany
  2. 2.Chair of Solid Mechanics, School of Mechanical Engineering and Safety EngineeringUniversity of WuppertalWuppertalGermany

Section editors and affiliations

  • Hans-Christian Möhring
    • 1
  1. 1.Institut für WerkzeugmaschinenUniversität StuttgartStuttgartGermany