This is Julia code for the nonsmooth primal-dual method for PDE constraint problems explained in the manuscript found here: https://arxiv.org/abs/2211.04807. Setup The code was written for Julia 1.6.7 and package dependencies are available in the .toml-file. To run the code start Julia in the codes root folder (where this readme.md file is located) using the command Julia --project=/path/to/code where the /path/to/code is replaced by the actual location on your machine. In the Julia REPL type ] to enter Pkg mode and type instantiate to download and install all the listed dependencies. Running the Examples There are 4 experiment files: Numerical0__.jl with __ being 1 or 2 and a or b. a corresponds to a coarse grid problem, b to a finer grid problem. To run an experiment pick one of the files. Creating the near-convergence solution to compare against To perform the same experiment as in the manuscript you will first need to do the long run computation so we have a target solution to compare against. To do that open the Experiment file and edit lines 20-21. Set load_conv_x to false and create_conv_x to true. Then call Julia replacing with the .jl file you just edited. Running the experiment After having done the long run above, edit the file's lines 20-21 again and set load_conv_x to true and create_conv_x to false. Then, as above, call Julia , where is the file you edited. The output can be found in the Numerical/vizY__/ folder where each run's results are sorted into a timestamped subdirectory.