Dune-UDG: a cut-cell framework for unfitted discontinuous Galerkin methods. Simulations on complex shaped domains are of big interest as the mesh generation for such domains is still an involved process. Recently, cut-cell based methods are becoming very popular. These methods avoid the problems of mesh-generation by using unfitted discretizations on cut-cell meshes. We present the Dune-UDG module which allows an easy implementation of Unfitted Discontinuous Galerkin methods on cut-cell grids. Different geometry representations are available. Using the presented interfaces it is possible to implement completely new cut-cell representations with a minimum of work.

References in zbMATH (referenced in 8 articles )

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  1. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  2. Christoph Lehrenfeld, Fabian Heimann, Janosch Preuß, Henry von Wahl: ngsxfem: Add-on to NGSolve for geometrically unfitted finite element discretizations. (2021) not zbMATH
  3. Engwer, Christian; Westerheide, Sebastian: An unfitted dG scheme for coupled bulk-surface PDEs on complex geometries (2021)
  4. Neiva, Eric; Badia, Santiago: Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems (2021)
  5. Engwer, Christian; May, Sandra; Nüßing, Andreas; Streitbürger, Florian: A stabilized DG cut cell method for discretizing the linear transport equation (2020)
  6. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  7. Lehrenfeld, Christoph; Reusken, Arnold: High order unfitted finite element methods for interface problems and PDEs on surfaces (2017)
  8. Lehrenfeld, Christoph: High order unfitted finite element methods on level set domains using isoparametric mappings (2016)