# Question about Variational Formulation
**URL:** https://community.freefem.org/t/question-about-variational-formulation/1059
**Category:** General Discussion
**Created:** [June 25, 2021, 8:45am UTC](https://community.freefem.org/t/question-about-variational-formulation/1059 "2021-06-25T08:45:11Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Aicha](https://community.freefem.org/u/Aicha)
#### Post date: [June 25, 2021, 8:45am UTC](https://community.freefem.org/t/question-about-variational-formulation/1059/1 "2021-06-25T08:45:11Z")
Hi!
i have two questions please
Q\_T = [0,L] x [0,H] x [0,T]
1- We have the following variational formulation:
\int\_{Q\_T} dV/dt \psi dx dy dt = - D \int\_{Q\_T} \nabla V . \nabla \psi dx dy dt + D \int\_0^T \int\_0^L \psi(x,0,t) (\gamma VC - h Vf) dx dt - u0 \int\_{Q\_T} y \dV/dx \psi dx dy dt - \sigma\_2 \int\_{Q\_T} V \psi dx dy dt
is it’s following formulation with FF++ is correct
```auto
problem system2(V,VH,solver=UMFPACK)=
int2d(Th)(V*VH/dt)+int2d(Th)(D*(dx(V)*dx(VH)+dy(V)*dy(VH)))
+int2d(Th)(u0*y*dx(V)*VH)+int2d(Th)(sigma2*V*VH)
-int2d(Th)(oldV*VH/dt)
+int1d(Th,1)(D*h*Vf*VH)-int1d(Th,1)(D*gamma*VC*VH);
```
2- what is the mathematical problem corresponding to the FF++ formulation:
`problem extend(Vk,Vt) = int2d(Th)(dy(Vk)*dy(Vt)) + on(1,Vk=V);`
Regards
---
### Author:  [@Aicha](https://community.freefem.org/u/Aicha)
#### Post date: [June 27, 2021, 11:02am UTC](https://community.freefem.org/t/question-about-variational-formulation/1059/2 "2021-06-27T11:02:51Z")
I add that
```auto
mesh Th = square(N,N,[L*x,H*y]);
fespace Vh(Th,P1);
```