Implementation of hp-adaptive discontinuous finite element methods in Dune-Fem

by   Christoph Gersbacher, et al.

In this paper we describe generic algorithms and data structures for the implementation of hp-adaptive discontinuous finite element methods in the Dune-Fem library. Special attention is given to the often tedious and error-prone task of transferring user data during adaptation. Simultaneously, we generalize the approach to the restriction and prolongation of data currently implemented in Dune-Fem to the case of p- and hp-adaptation. The dune-fem-hpdg module described in this paper provides an extensible reference implementation of hp-adaptive discontinuous discrete function spaces. We give details on its implementation and the extended adaptive interface. As proof of concept we present the practical realization of an hp-adaptive interior penalty method for elliptic problems.


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