Finite element approximation

In this section we study certain linear classes V of approximating functions resp. sequences of them {V j , j = 0, 1, ...} which are particularly useful for efficient numerical methods in different fields. They share some properties which can be described in short as follows: existence of a well-localized and stable (with respect to L p -norms) algebraic basis, simple recursions (prolongation and restriction operators) for exchanging information between different V j , good approximation properties for smooth functions, e.g., from Sobolev spaces.