# Finite Element Methods

Finite Element Methods

In mathematics, finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. It uses variational methods (the Calculus of variations) to minimize an error function and produce a stable solution. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain.

Read more about Finite Element Methods:  History, Discretization, Comparison To The Finite Difference Method, Application

### Other articles related to "finite element methods, element, elements, methods":

Extended Finite Element Method - Principle
... Enriched finite element methods extend, or enrich, the approximation space so that it is able to naturally reproduce the challenging feature associated with the problem of interest the ... Moreover, treating problems with discontinuities with eXtended Finite Element Methods suppresses the need to mesh and remesh the discontinuity surfaces, thus alleviating the computational costs and projection errors ...
Systematic Element Name
... A systematic element name is the temporary name and symbol assigned to newly synthesized and not yet synthesized chemical elements ... In chemistry, a transuranic element receives a permanent name and symbol only after its synthesis has been confirmed ... some cases, this has been a protracted and highly political process (see element naming controversy) ...
Element - Philosophy
... Alchemical elements, the components of the universe, expressed in their Aristotelian forms as fire, earth, air, wood, and water Bhūta are five elements in Hinduism The ...
Finite Element Methods - Application
... FEM allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements ... FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system ...
Spectral Method
... Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, often involving the use of the ... Spectral methods and finite element methods are closely related and built on the same ideas the main difference between them is that spectral methods use basis functions that are nonzero over ... In other words, spectral methods take on a global approach while finite element methods use a local approach ...

### Famous quotes containing the words methods, finite and/or element:

All men are equally proud. The only difference is that not all take the same methods of showing it.
François, Duc De La Rochefoucauld (1613–1680)

We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.
Blaise Pascal (1623–1662)

The reverence for the Scriptures is an element of civilization, for thus has the history of the world been preserved, and is preserved.
Ralph Waldo Emerson (1803–1882)