2. Discrete Problems and Discretization

Discretization considers the fact that analytical methods which are known from functional analysis cannot be directly applied to functions stored in a computer, and an assumption on the functional structure of the single elements has to be made.

One main aspect of this chapter is the development of a formalism which is designed for writing expressions in the context of discretization. It is shown that such a formalism can be used for a concise definition of the topological as well as the functional structure of the respective discretization formulae. This formalism can be used for the specification of computer programs, when such a formalism contains sufficient information to carry out all operations which are required for the evaluation of the formulae.