@dokken
In fact the problem comes from the use of the Discontinuous Galerkin in order to impose a constraint through a Lagrange multiplier which is not the right way.
It seems that I must use dolfinx_mpc.
However, it is not clear how to implement it for non linear problems.
There is this conversation and this one, but the file test_nonlinear_assembly.py seems not to correspond to the latest versions of dolfinx… ?