Finite element method

In numerical analysis, the finite element method (FEM) is used for solving partial differential equations (PDE) approximately. Solutions are approximated by either eliminating the differential equation completely (steady state problems), or rendering the PDE into an equivalent ordinary differential equation, which is then solved using standard techniques such as finite differences, etc. The use of the finite element method in engineering for the analysis of physical systems is commonly known as finite element analysis.

Related Topics:
Numerical analysis - Partial differential equation - Ordinary differential equation - Finite difference - Finite element analysis

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Finite element methods have also been developed to approximately solve integral equations such as the heat transport equation.

Related Topics:
Integral equation - Heat

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The method was introduced by Richard Courant to model the effect of torsion on the shape of a cylinder. Courant's contribution was evolutionary, drawing on a large body of earlier results for PDEs developed by Rayleigh, Ritz, and Galerkin. Development of the method began in earnest in the middle to late 1950s for airframe and structural analysis, and picked up a lot of steam at Berkeley in the 1960s for use in civil engineering. The method was provided with a rigorous mathematical foundation in 1973 with the publication of Strang and Fix's An Analysis of The Finite Element Method.

Related Topics:
Richard Courant - Torsion - Cylinder - Rayleigh - Ritz - Galerkin - 1950s - Airframe - Structural analysis - Berkeley - 1960s - Civil engineering - 1973 - Strang

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Finite element methods are used in a wide variety of engineering disciplines, e.g., electromagnetics.

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In solving partial differential equations, the primary challenge is to create an equation which approximates the equation to be studied, but which is numerically stable, meaning that errors in the input data and intermediate calculations do not accumulate and cause the resulting output to be garbage.

Related Topics:
Partial differential equation - Numerically stable

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