FreeFem++

[Walid8824]

Dear All,

I am totally new to freefem++ and trying to solve 4 PDEs in 2D. My problem is the system is unstable and can not converge I use Problem statement. I am not sure I should move to stabilization techniques or PETSc
when I change the variational form writing from problem to varf the solution is not correct at all even at the first steps.
I attached my code and also copy and paste the two ways I am trying to write the variational form with (problem , varf ) stament

My questions are
1- why when I change from problem to varf the results is changed
2- should I use PETSc or move to stabilization techniques like SUPG or artificial diffusion

problem HydrodynamicNe(Ne, v1) = int2d(Th)(Nev1
+(Dedt*(grad(Ne)'grad(v1))
+(-Wex * dx(Ne) + -Wey * dy(Ne))dtv1))
-int2d(Th)(Neoldv1)
-int2d(Th)(Sev1dt)
+int1d(Th,needle)(gammaNpoldmupEmagv1*dt)
;

varf HydrodynamicNe(Ne, v1) = int2d(Th)(Nev1
+(Dedt*(grad(Ne)'grad(v1))
+(-Wex * dx(Ne) + -Wey * dy(Ne))dtv1))
-int2d(Th)(Neoldv1)
+int2d(Th)(Sev1dt)
+int1d(Th,needle)(gammaNpoldmupEmagv1*dt)
;
matrix AE = HydrodynamicNe(Ve,Ve) ;
real [int] bE = HydrodynamicNe(0 ,Ve) ;

trail 1.log