01_obstacle_problem

Example 1 (Figure 3): The Obstacle Problem

Finite element method (proximal Galerkin)

Figures 3 (a) and (b) are generated with DOLFINx.

To reproduce the results in Figures 3 (a) (the comparison between Proximal Galerkin, SNES, Galahad, and IPOPT), first deploy the ghcr.io/methods-group/proximalgalerkin:v0.3.0 Docker container. Then execute the following scripts (in dolfinx-mode, see ../../README.md):

python3 generate_mesh_gmsh.py
python3 compare_all.py -P ./meshes/disk_1.xdmf -O coarse
python3 compare_all.py -P ./meshes/disk_2.xdmf -O medium
python3 compare_all.py -P ./meshes/disk_3.xdmf -O fine

Note

The comparison script requires both GALAHAD and IPOPT which are not supplied by the standard FEniCS/DOLFINx installation.

Proximal finite difference and spectral methods

To reproduce the finite difference and spectral method results in Figure 2 (c), deploy a container with Julia, for instance (julia:1.10.8 or ghcr.io/methods-group/proximalgalerkin).

julia obstacle_finite_difference.jl
julia obstacle_spectral.jl

If using the docker containers, you can most likely use the flag

julia --compiled-modules=existing obstacle_finite_difference.jl

to speed up the run-time.