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MooNMD – a program package based on mapped finite element methods. (English) Zbl 1061.65124
Summary: 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 the global degrees of freedom which define the finite element space. We 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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
74S05 Finite element methods applied to problems in solid mechanics
Software:
MooNMD; UG
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