Getting Problem to get Superconvergence results in Hybrid Higher Order (HHO) Method in Poisson Equation

General Discussion
1

Hello, all experts and respected professors,

I am facing a problem getting superconvergence results ( Need to get (k+2) order in L^2-norm and (k+1) in reconstruction gradient using P^k polynomial approx. ) for the Poisson equation by using HHO in FF++.

Here is the HHO scheme using the reconstruction operator :

eq1
eq11168×356 25 KB

eq2
eq21261×305 23.9 KB

Note that gamma=1 (in equation (2)).

Details paper:

Very_good.pdf (250.3 KB)

My Code:

HHO_best.edp (3.2 KB)

Results:

results
results803×553 10.9 KB

But i need 3 order in L2-norm and 2 order in reconstruction gradient. Why is the Superconvergence not coming??.

I really appreciate any help I get. Thanks in advance !.