Dear all,

I hope you are doing very well. I want to write a FreeFEM++ code to solve the Poisson Problem

-∆u=f in Ω

u=g on ∂Ω

using the Modified Weak Galerkin Finite Element Method mentioned in the paper:

[1] “A modified weak Galerkin finite element method”. X. Wang, N.S. Malluwawadu, F. Gao, T.C. McMillan.

https://www.sciencedirect.com/science/article/pii/S0377042714002131.

There is a FreeFEM++ code to solve this problem according to the Galerkin FEM, but there is no FreeFEM++ code to solve this problem according to Modified Weak Galerkin FEM. I would appreciate your help.

I did the following code, but the results are confusing. They are not the same as in the paper:

[1] A modified weak Galerkin finite element method. X. Wang, N.S. Malluwawadu, F. Gao, T.C. McMillan. https://www.sciencedirect.com/science/article/pii/S0377042714002131.

I am not sure about the jump function and the weak discrete gradient is the same in both the discontinuous Galerkin FEM and the modified Weak Galerkin FEM which is not defined at all in FreeFEM++.

MWGFEM_1.edp (1.2 KB)