Demonstration files

The python files in this directory provide several examples that demonstrate the usage of ngsxfem features. For an introduction to these features we refer to the ngsxfem-jupyter tutorials. In the next table you can see the available demonstration files and a short description:

filename	description
lsetgeoms.py	Examples of smooth domains described by level set functions and their geometrical approximation.
unf_interf_prob.py	Stationary scalar unfitted interface problem with an unfitted isoparametric FEM discretization and Nitsche.
fictdom.py	Poisson problem on an unfitted (smooth) domain described by a level set function, discretized with CutFEM, Ghost Penalties and Nitsche.
fictdom_dg.py	Poisson problem on an unfitted (smooth) domain described by a level set function, discretized with Cut-DG (interior penalty), Ghost Penalties and Nitsche.
fictdom_mlset.py	Poisson problem on an unfitted domain described by multiple level sets, discretized with CutFEM and Nitsche.
stokescutfem.py	Stationary Stokes interface problem with an unfitted isoparametric Taylor-Hood-Nitsche discretization
tracefem.py	stationary surface PDE problem with a TraceFEM discretization
fictdom_dg.py	Poisson problem on an unfitted (smooth) domain described by a level set function, discretized with a Cut Discontinuous Galerkin method and Nitsche.
moving_domain.py	Parabolic PDE on a moving domain solved by an Eulerian time stepping method using isoparametric CutFEM and Ghost penalty stabilization.
aggregates/aggfem_shapetester.py	Explanation of aggregated FEM basis functions as a means to deal with (small) cut elements.
aggregates/fictdom_aggfem.py	FEM basis aggregation to solve a fictitious domain problem (without ghost penalties).
aggregates/fictdom_dg_aggfem.py	DG basis aggregation (cell merging) to solve a fictitious domain problem (without ghost penalties).
spacetime/spacetimeDG_fitted.py	Parabolic PDE on a stationary fitted domain solved by a space-time DG-in-time method.
spacetime/spacetimeDG_unfitted.py	Parabolic PDE on a moving domain solved by a an unfitted isoparametric space-time DG-in-time CG-in-time method.
spacetime/spacetimeCG_unfitted.py	Parabolic PDE on a moving domain solved by a an unfitted isoparametric space-time continuous-in-time CG-in-time Petrov-Galerkin method.
spacetime/spaceDGtimeDG_unfitted.py	Parabolic PDE on a moving domain solved by a an unfitted isoparametric space-time DG-in-time DG-in-time method.
spacetime/spaceDGtimeDG_unfitted_3D.py	Parabolic PDE on a moving domain solved by a an unfitted isoparametric space-time DG-in-time DG-in-time method (3D).
spacetime/spacetime_vtk.py	Demonstration on how to export functions on a (2D+time) time slab to a vtk output.
spdes/surfstokestracefem.py	TraceFEM discretization of the Stokes equations on a level set surface.
mpi/mpi_nxfem.py	MPI version of a solution of a scalar unfitted interface problem in Nitsche-XFEM formulation.