A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

A means of solving ordinary and partial differential equations through discretization of the defining differential equations into elements. Individual element mass and stiffness matrices are assembled and from them global stiffness and mass matrices are assembled and used to solve the coupled system. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

The methods discretize a complex physical system as a set of many elements having a very simple geometrical shape (e.g. a triangle-shaped plate), for which it it is simple to solve the differential equation. A global mass and stiffness matrix are then formed from the element matrices and used to solve the system

See Wikipedia page on FEMs.

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