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The '''finite element method''' ('''FEM''') is an extremely popular method for numerically solving [[differential equation]]s arising in engineering and [[mathematical models|mathematical modeling]]. Typical problem areas of interest include the traditional fields of [[structural analysis]], [[heat transfer]], [[fluid flow]], mass transport, and [[electromagnetic potential]].
The FEM is a general [[numerical analysis|numerical method]] for solving [[partial differential equations]] in two or three space variables (i.e., some [[boundary value problem]]s). To solve a problem, the FEM subdivides a large system into smaller, simpler parts called '''finite elements'''. This is achieved by a particular space [[discretization]] in the space dimensions, which is implemented by the construction of a [[Types of mesh|mesh]] of the object: the numerical ___domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of [[algebraic equation]]s. The method approximates the unknown function over the ___domain.<ref>{{cite book
| title = A first course in the finite element method
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