# MooNMD

The basis of mapped finite element methods are reference elements where the components of a local finite element are defined. The local finite element on an arbitrary mesh cell will be given by a map from the reference mesh cell.\parThis paper describes some concepts of the implementation of mapped finite element methods. From the definition of mapped finite elements, only local degrees of freedom are available. These local degrees of freedom have to be assigned to the global degrees of freedom which define the finite element space. We present an algorithm which computes this assignment.\parThe second part of the paper shows examples of algorithms which are implemented with the help of mapped finite elements. In particular, we explain how the evaluation of integrals and the transfer between arbitrary finite element spaces can be implemented easily and computed efficiently.