Preprint series: 02-01, Technical Reports
- 65Y99 None of the above but in this section
Abstract: 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. This 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 theglobal degrees of freedom which define the finite element space. We will present an algorithm which computes this assignment. The 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.
Keywords: mapped finite elements, degrees of freedom, transfer between arbitrary finite element spaces
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