Definitions for

**"Finite element method"**A numerical approximation method in which data is represented over some domain by a discrete series of functions. The domain is divided into a finite number of subregions called elements, whence the name. A series of functions is built up by defining a simple function, e.g. a low-order polynomial, on each element and requiring continuity between functions on adjacent subregions. The points where values are used to define the functions are conventionally called nodes and the defining parameters nodal values. Finite elements are distinguished from spectral methods in that their approximations are local and not global, and they are distinguished from finite differences because the function is defined over a whole region rather than just a discrete points. Their use is more prevalent in modeling solid structures such as buildings or airplanes than it is for geophysical fluid flow, although several authors have constructed circulation models using finite elements. Perhaps their greatest advantage is the relative ease with which highly irregular boundaries can be handled as opposed to with the aforementioned spectral and finite difference methods.

(n.) An approximate method for solving partial differential equations by replacing continuous functions by piecewise approximations defined on polygons, which are referred to as elements. Usually polynomial approximations are used. The finite element method reduces the problem of finding the solution at the vertices of the polygons to that of solving a set of linear equations. This task may then be accomplished by a number of methods, including Gaussian elimination, the conjugate gradient method and the multigrid method. See also finite difference method.

This is the method used in RTM-Worx to discretize the partial differential equations that describe conservation of mass, momentum and energy into a linearised set of equations that can be solved numerically. The geometry is subdivided into smaller objects, so-called elements, in which the resin velocity is constant and pressure varies linearly.