Definition:Finite Element Method
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Definition
The finite element method is a technique for approximating the solution to a partial differential equation with boundary conditions over a given domain $D$.
$D$ is partitioned into elements, typically:
- triangles for a $2$-dimensional domain
- tetrahedra for a $3$-dimensional domain.
On each element the solution is approximated by an appropriate function, usually a polynomial of small degree.
The coefficients that define the polynomials are chosen to satisfy a best approximation criterion
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Also see
- Results about the finite element method can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): finite element method