The dune-udg module allows for an easy implementation of Unfitted Discontinuous Galerkin methods on cut-cell grids.
It offers integration with dune-pdelab.
It has been used to solve
- elliptic and parabolic PDEs using the UDG method
- elliptic PDEs using ghost-penalty stabilized CutFEM
- UDG for surface PDEs, using similar concepts as Trace-FEM
- linear hyperbolic conservation law using a stabilized Cut-DG method
Publications and Documentation
The UDG method is published in
P. Bastian, C. Engwer. An unfitted finite element method using discontinuous Galerkin. International Journal for Numerical Methods in Engineering, 79(12), 2009 , 1557-1576
- Ch. Engwer, An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling, Heidelberg University, 2009. (PDF)
An older implementation of dune-udg is described in
C. Engwer, F. Heimann. Dune-UDG: A Cut-Cell Framework for Unfitted Discontinuous Galerkin Methods. Advances in DUNE, , 2012 , 89-100