# Understanding problem
**URL:** https://community.freefem.org/t/understanding-problem/2684
**Category:** General Discussion
**Created:** [September 5, 2023, 11:09am UTC](https://community.freefem.org/t/understanding-problem/2684 "2023-09-05T11:09:46Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@moufide](https://community.freefem.org/u/moufide)
#### Post date: [September 5, 2023, 11:09am UTC](https://community.freefem.org/t/understanding-problem/2684/1 "2023-09-05T11:09:46Z")
Good evening everyone
I would like to understand this code:
// Parameters
func u0 = 10. + 90._x/6.;
func k = 1.8_(y\<0.5) + 0.2;
real ue = 25.;
real alpha=0.25;
real T=5.;
real dt=0.1 ;
// Mesh
mesh Th = square(30, 5, [6.\*x,y]);
// Fespace
fespace Vh(Th, P1);
Vh u=u0, v, uold;
// Problem
problem thermic(u, v)
= int2d(Th)(
u\*v/dt
- k\*(
dx(u) \* dx(v)
- dy(u) \* dy(v)
)
)
- int1d(Th, 1, 3)(
alpha_u_v
)
- int1d(Th, 1, 3)(
alpha_ue_v
)
- int2d(Th)(
uold\*v/dt
)
- on(2, 4, u=u0)
;
// Time iterations
ofstream ff(“thermic.dat”);
for(real t = 0; t \< T; t += dt){
uold = u; //equivalent to u^{n-1} = u^n
thermic; //here the thermic problem is solved
ff \<\< u(3., 0.5) \<\< endl;
plot(u);
}
I would like to understand this line “uold = u; //equivalent to u^{n-1} = u^n” after this line what is the value of u,?.
Is u still unknown?
I want to evaluate the L2 norm of the derivative of the solution, that is to say each time I want to calculate (u^n+1-u^n)/dt.
Will this value of the derivative not always be zero ?
---
### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [September 5, 2023, 3:39pm UTC](https://community.freefem.org/t/understanding-problem/2684/2 "2023-09-05T15:39:18Z")
No and No because at this stage u is not update to the next value.
so you save le previous value .
After thermic you compute the next value of u ( u at t = t+ dt)
and uold value of u at time t.
(u-uold)/dt is a approximation of the time derivative in this case.