Bibliographic record for `Bangerth:2009:DSR'

@Article{Bangerth:2009:DSR,
  author =       "W. Bangerth and O. Kayser-Herold",
  title =        "Data Structures and Requirements for $hp$ Finite Element Software",
  journal =      "{ACM} Transactions on Mathematical Software",
  accepted =     "22 August 2008",
  upcoming =     "true",
  abstract =     "Finite element methods approximate solutions of partial differential equations by restricting the problem to a 
                 finite dimensional function space. In $hp$ adaptive finite element methods, one defines these discrete spaces by 
                 choosing different polynomial degrees for the shape functions defined on a locally refined mesh.
                 \par Although this basic idea is quite simple, its implementation in algorithms and data structures is challenging. 
                 It has apparently not been documented in the literature in its most general form. Rather, most existing implementations
                 appear to be for special combinations of finite elements, or for discontinuous Galerkin methods.
                 \par In this paper, we discuss generic data structures and algorithms used in the implementation of $hp$ methods for 
                 arbitrary elements, and the complications and pitfalls one encounters. As a consequence, we list the information a
                 description of a finite element has to provide to the generic algorithms for it to be used in an $hp$ context. We 
                 support our claim that our reference implementation is efficient using numerical examples in 2d and 3d, and
                 demonstrate that the $hp$ specific parts of the program do not dominate the total computing time. This reference 
                 implementation is also made available as part of the Open Source deal.II finite element library.",
}