Article
Article
- Mathematics
- Applied mathematics
- Finite element method
- Engineering & Materials
- Engineering and materials - general
- Finite element method
Finite element method
Article By:
Balderes, Theodore Northrop Grumman Aerospace Corporation, Bethpage, New York.
Last reviewed:June 2020
DOI:https://doi.org/10.1036/1097-8542.257700
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- Finite element method, published January 2014:Download PDF Get Adobe Acrobat Reader
- Development
- Mathematical methods
- Element formulation and types
- Application and implementation procedure
- Related Primary Literature
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A numerical analysis technique for obtaining approximate solutions to many types of engineering problems. The need for numerical methods arises from the fact that for most engineering problems analytical solutions do not exist. While the governing equations and boundary conditions can usually be written for these problems, difficulties introduced by either irregular geometry or other discontinuities render the problems intractable analytically. To obtain a solution, the engineer must make simplifying assumptions reducing the problem to one that can be solved, or a numerical procedure must be used. In an analytic solution, the unknown quantity is given by a mathematical function valid at an infinite number of locations in the region under study, while numerical methods provide approximate values of the unknown quantity only at discrete points in the region. In the finite element method, the region of interest is divided into numerous connected subregions or elements within which approximating functions (usually polynomials) are used to represent the unknown quantity (Fig. 1). See also: Mathematics; Polynomial systems of equations
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