# How assignment operator works for discontinuous fields

**URL:** https://community.freefem.org/t/how-assignment-operator-works-for-discontinuous-fields/1093
**Category:** General Discussion
**Created:** [July 12, 2021, 7:50pm UTC](https://community.freefem.org/t/how-assignment-operator-works-for-discontinuous-fields/1093 "2021-07-12T19:50:54Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![arousta](https://avatars.discourse-cdn.com/v4/letter/a/838e76/32.png) [@arousta](https://community.freefem.org/u/arousta)
#### Post date: [July 12, 2021, 7:50pm UTC](https://community.freefem.org/t/how-assignment-operator-works-for-discontinuous-fields/1093/1 "2021-07-12T19:50:54Z")

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The documentation says the = operator does interpolation. But not clear on what happens when interpolating discontinuous fields. For example:

```auto
mesh Th = square(1,1);
fespace Vh0(Th,P0);
fespace Vh1(Th,P1);

Vh0 F0 = x;
Vh1 F1 = F0;
Vh1 F1p, q;

plot(F0,fill=1,value=1,dim=3,wait=1);
plot(F1,fill=1,value=1,dim=3,wait=1);

solve proj(F1p,q) = int2d(Th)(F1p*q)-int2d(Th)(F0*q);
plot(F1p,fill=1,value=1,dim=3);

```

One way to go from P0 to P1 field is using a projection which gives F1p.

But for doing interpolation (F1) the value should be computed on points. I’m wondering how the “=” operator computes the values at diagonals? Here we have two different values and it doesn’t average them. Is it picking randomly one of the values of F0 to assign F1?