# Error between numerical solutions

Hey guys,

is it possible to compute the error between two numerical solutions in freefem?
Say I have a problem without an exact solution, but I can do a reference one using a refined mesh, can a compute the error (L2, H1,…)?

Yes, you can

FreeFEM can do the interpolation for you from mesh 1 onto mesh 2 simply by writing

`u_mesh2 = u_mesh1`

I tried that. I compile a reference solution and saved in a file. Then, I want read from that file and use as an exact solution to compare to results in a coarse mesh, like this

``````ifstream fileR(filename);
fileR >> u[];
``````

but I’m getting the following error:

``````length on the array 6 != 153 length in file
current line = 523
-- number :1
-- number :1
err code 8 ,  mpirank 0
``````

do you have an ideia of what might be?

Hi,
you have to declare `u` in the `fespace` used to save the reference solution (the `fespace` on the fine mesh).
Then `fileR >> u[];` recovers the reference solution on the fine mesh
You can afterwards declare `v` in the `fespace` on the coarse mesh, and write
v=u;
so that v will contain the interpolation of `u` on the coarse mesh.
At end you can compute for example
`real error=sqrt(int2d(Th)((ucomp-v)^2));`
where `ucomp` is your computed solution on the coarse mesh `Th`.
An important point is that you need to have both meshes at hand in order to do it. Hence you need to save not only the reference solution, but also the (fine) mesh that comes with it.

1 Like

I use triangulate and a text file with (x,y,value) lines.
I guess you could put this table mesh in a scoped block and
assign the result to a target fespace. This code appears to work
although it could be cleaned up a bit

``````macro mmloadds(u,Th,fn,nthings,nentry)
{
Th =triangulate(fn);
/* this needs to be a P1 space */
fespace Vhxxx(Th,P1);
Vhxxx data;
real[int] mdata(Th.nv);
try{
ifstream ifs(fn);
real xass;
for (int i=0; i<Th.nv; ++i)
{
for (int j=0; j<nthings; ++j)
{ if (j==nentry) ifs>> mdata[i];
else ifs>> xass;
}
}
} catch (...) { cout<<" throw during load of "<<fn<<endl; cout.flush;  }
data=0;
data[]=mdata;
u=0;
u=data;