Abstract: The theory of finite element methods is one of the success stories of modern mathematics. It is therefore reasonable to ask what set-valued numerical analysis can learn from this field. The main aim of this talk is to popularise the concept of set spaces that are defined in terms of a generalization of the well-known support function. This concept seems to be the language in which the central ideas behind finite element methods can be transferred to the computation of sets. After a formal introduction to set spaces, some graphic examples of such spaces will be given, and the relationship between conventional representations of sets and set spaces will be explained. Some preliminary results will be shown and commented.