A method for continuous approximation of discretely given data in a tw
o- or three-dimensional domain of arbitrary shape is presented. The me
thod uses shape functions of customary finite elements for modelling t
he approximation; special properties ensure the smoothness for success
ful differentiating and improve the accuracy. Many ideas and tools fro
m finite element analysis can be used and the presented examples show
the easy application. No restriction is made to the input data, scalar
- or vector-valued, and especially the distribution of the given data,
can be totally irregular (scattered data). Hence, the method is appli
cable to a wide range of problems. (C) 1997 Elsevier Science Ltd.