05 Fakultät Informatik, Elektrotechnik und Informationstechnik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/6

Browse

Subject: search.filters.subject.510End date: 2011

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Generalizations of the finite element method
    (2011) Schweitzer, Marc
    This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.
  • Thumbnail Image
    ItemOpen Access
    Discontinuous Galerkin methods for two-phase flows in porous media
    (2010) Grüninger, Christoph
    In this work two-phase flows in porous media are simulated numerically with Discontinuous Galerkin methods. The three methods Symmetrical Interior Penalty Galerkin method (SIPG), Non-symmetrical Interior Penalty Galerkin method (NIPG) and the scheme from Oden, Babuška and Baumann (OBB) are considered. The terminology and the examples are taken from soil science. First the Richards equation is solved using these methods. Then a two-phase flows problem in the saturation/pressure formation is solved with OBB and NIPG. The numerical methods are implemented using the software toolkit PDELab. They are tested with examples from other publications. Weighted averages for absolute and relative permeabilities are examined.