Getting Problem to get good convergence rate in Proximal Discontinuous Galerkin method of Elliptic obstacle problem

General Discussion
1

Respected Professors and experts,

I am trying to get a good convergence rate using the Proximal Discontinuous Galerkin(PDG) method for the elliptic obstacle problem.

Here is my main scheme:

PDG_scheme
PDG_scheme996×968 161 KB

Data for numerical experiments:

image
image1115×428 61.6 KB

image

Here, is my IPDG proximal galerkin code:

PDG_elliptic.edp (4.0 KB)

Note: The code runs correctly, but the results are not satisfactory. Additionally, how can the following space be defined in the code for the proximal EG method?.

image
image1072×130 21.3 KB

(How to write this Vh space in the FF++ code for Proximal EG method ?.)

Here is the full paper of proximal discontinuous Galerkin method of elliptic obstacle problem:

Proximal_dg_2026.pdf (503.2 KB)

I would be very grateful for any suggestions to obtain the expected order of convergence, i.e., 2, in the L^2-norm.