How to implement the lifting operator?

General
1

Hi everyone

I want to use the LDG to solve the Poisson problem, but I don’t know how to implement the lifting operator in FEniCS. I’ve searched online for a long time without finding an answer. Has anyone worked on this type of problem before?

Discrete gradient operators
Discrete gradient operators1058×524 41.9 KB

For all \left(v_h, w_h\right) \in V_h^k \times V_h^k, consider the following symmetric DG bilinear form
a_h\left(v_h, w_h\right) \stackrel{\text { def }}{=} \int_{\Omega} G_h\left(v_h\right) \cdot G_h\left(w_h\right)+j_h\left(v_h, w_h\right)

From my understanding, I need to solve equation (10) for each basis function in the DG space.

Thanks!