Finite element analysis (FEA) or finite element method (FEM) is a numerical technique for solution of boundary-value problems. It was first developed in the late forties for use in structural analysis. In its application, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions—i.e., finite elements. Equations of equilibrium, in conjunction with applicable physical considerations such as compatibility and constitutive relations, are applied to each element, and a system of simultaneous equations is constructed. The system of equations is solved for unknown values using the techniques of linear algebra or nonlinear numerical schemes, as appropriate. While being an approximate method, the accuracy of the FEA method can be improved by refining the model using more elements and nodes. In numerical analysis, the finite element method (FEM) is used for solving partial differential equations (PDE) approximately. ... See also: structuralism. ... The term compatibility has the following meanings: In telecommunication, the capability of two or more items or components of equipment or material to exist or function in the same system or environment without mutual interference. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ...

A common use of FEA is for the determination of stresses and displacements in mechanical objects and systems. However, it is also routinely used in the analysis of many other types of problems, including those in heat transfer, fluid dynamics and electromagnetism. FEA is able to handle complex systems that defy closed-form analytical solutions. This article is in the process of being merged into Heat, and may be outdated. ... This article or section should be merged with Fluid mechanics Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

External links

There are many commercially available FEA software packages, including ABAQUS, Ansys, Nastran and Marc.

• NEiNastran FEA (http://www.nenastran.com)
• ABAQUS, Inc. (http://www.abaqus.com)
• NAFEMS - The International Association for the Engineering Analysis Community (http://www.nafems.org)
• ANSYS, Inc. (http://www.ansys.com)
• MSC Software (Nastran and Marc) (http://www.mscsoftware.com/products/products.cfm?Q=132&Z=149)
• LSTC (provide LS-Dyna) (http://www.lstc.com)