# Error of two solutions

**URL:** https://community.freefem.org/t/error-of-two-solutions/63
**Category:** General Discussion
**Created:** [May 30, 2019, 6:42pm UTC](https://community.freefem.org/t/error-of-two-solutions/63 "2019-05-30T18:42:51Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![Aicha](https://avatars.discourse-cdn.com/v4/letter/a/ec9cab/32.png) [@Aicha](https://community.freefem.org/u/Aicha)
#### Post date: [May 30, 2019, 6:42pm UTC](https://community.freefem.org/t/error-of-two-solutions/63/1 "2019-05-30T18:42:51Z")

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Hi,  
i have to calculate in 3D solutions u and w of two problems:  
du/dt - \Delta u = f and dw/dt - Delta w +w =f , (x,y,z) \in (0,1)^3, t \in [0,1]  
where f(x,y,z)= 0.25\*sin(2\*pi\*x)   
and calculate the norme H^1 of the difference between u and w.  
There is what i try. Is it correct?  
Kind regards

’ ’ ’ freefem  
load “UMFPACK64”  
defaulttoUMFPACK64();

load “iovtk”

load “msh3”

verbosity=1;

func real f (real x)  
{  
return 0.25_sin(2_pi\*x);  
};

real t=0.00;  
real dt=0.1;

mesh3 Th=cube(20,20,20);  
fespace Vh(Th,P1,periodic=[[1,x,z],[3,x,z],[2,y,z],[4,y,z],[5,x,y],[6,x,y]]);  
fespace Wh(Th,P2,periodic=[[1,x,z],[3,x,z],[2,y,z],[4,y,z],[5,x,y],[6,x,y]]);  
Vh uh=0.0;  
Vh wh=0.0;  
Vh vh;  
Vh oldU=0.0;  
Vh oldW=0.0;  
real T=1.0;// arbitraire  
int[int] Order= [1];

Vh fh=f;

// Nonlinear part is calculated in previous iteration (nith) and becomes a part of the right hand side  
problem het(uh,vh,init=t) =  
int3d(Th)((dx(uh)_dx(vh)+dy(uh)dy(vh)+dz(uh)dz(vh))dt)  
+int3d(Th)(uhvh)  
-int3d(Th)(oldUvh)  
-int3d(Th)(fhvh_dt)  
;

problem hom(wh,vh,init=t) =  
int3d(Th)((dx(wh)_dx(vh)+dy(wh)dy(vh)+dz(wh)dz(vh))dt)  
+int3d(Th)(whvh)  
-int3d(Th)(oldWvh)  
+int3d(Th)(whvh_dt)  
-int3d(Th)(fh_vh_dt)  
;

for (t=0;t\<=T;t+=dt) {  
fh=f(t);  
oldU=uh;  
het;  
}

for (t=0;t\<=T;t+=dt) {  
fh=f(t);  
oldW=wh;  
hom;  
}  
real errH1 = sqrt(int3d(Th)(square(uh - wh)) + int3d(Th)(square(dx(uh)-dx(wh)) + square(dy(uh)-dy(wh))+ square(dz(uh)-dz(wh))));  
cout \<\< " errH1 = "\<\< errH1 \<\<endl;