Difference between revisions of "Finite element method"

Latest revision as of 08:39, 4 April 2017

The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. It is also referred to as finite element analysis (FEA).

Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.

The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. The finite element method formulation of the problem results in a system of algebraic equations. The method yields approximate values of the unknowns at discrete number of points over the domain.

To solve the problem, it subdivides a large problem into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

See also

• Applied element method
• Boundary element method
• Computer experiment
• Direct stiffness method
• Discontinuity layout optimization
• Discrete element method
• Finite difference method
• Finite element machine
• Finite element method in structural mechanics
• Finite volume method
• Finite volume method for unsteady flow
• Interval finite element
• Isogeometric analysis
• Lattice Boltzmann methods
• List of finite element software packages
• Movable cellular automaton
• Multidisciplinary design optimization
• Multiphysics
• Patch test
• Rayleigh–Ritz method
• Space mapping
• Weakened weak form

External links

• Finite element method @ Wikipedia