# 2. 4 Topological Mappings of Shape Functions

In this section the function space introducted in the former sections is founded on the definition of the cell complex . Once the cell complex is established and available within the framework of the computer, weighting coefficients can be stored in association with the underlying cell complex and a function (which is an element of a predefined function space) is established.

Again, it has to be stated that such an interpretation of a function stored in a computer completely differs from the function by point interpretation, which is used in most methods based on finite differences [57] or finite volumes [58].

A basic data structural requirement for the specification of the function space based on a cell complex is that data can be associated with single elements of the cell complex. In general, one or more mappings between elements of the basis of the cell complex and some numeric data are used. Such a function might be defined as follows:

 (2.27)

A function which assigns an element of the cell complex a numerical value is called a quantity. It is also possible that such a function is only defined on a partial set of the cell complex. The domain of definition has to be given explicitly in order not to obtain invalid function values (see Fig. 2.6).

 (2.28)

Subsections
Michael 2008-01-16