Hello, I have a problem formulation in this (simplified) form :

Where u_primal is a known vector, and u_dual v_dual are test and trial functions.

In order to solve this problem on NGSolve, I use the Lax-Milgram theorem to change the weak formulation.

The aim is now to to solve this problem.

The way I did this is :

```
def run_dual(gfRho,gfu_primal):
gfu_dual = GridFunction(V2)
# Known value of the integral since u_primal is known
first_integral=([val**(1/exp - 1) for val in Integrate(gfRho * stress(gfu_primal) ,mesh, element_wise=True)])
# Lax Milgram formulation
aNRJ=BilinearForm(V2, symmetric=True,check_unused=False)
# Right part of the formula (with epsilon(u) : epsilon(v))
aNRJ+=SymbolicEnergy((1/2)*(InnerProduct((Sym(Grad(v_dual))), Sym(Grad(v_dual)))), definedon=mesh.Materials("active"))
# Left part of the formula
aNRJ+=SymbolicEnergy(-1 * first_integral * stress(v_dual) , definedon=mesh.Materials("active"))
# Solver
solveStateEquationEnergy(gfu_dual,4,aNRJ,V2, dampfactor=0.1,maxit=40,maxerr=0.5e-8)
return gfu_dual
```

My question is the following : The way I implemented the first integrale (at the 1/exp - 1 power) is for sure wrong. I don’t have any clue on how to achieve it and write the exact same way my formula. Can you please help me to achieve implementing this formula ?

I am sure that the first part (left part of formula) is correct, the error is how I wrote the left part of the formula.

Thanks a lot !