# Finding the maximum of a function on the mesh

**URL:** https://community.freefem.org/t/finding-the-maximum-of-a-function-on-the-mesh/1438
**Category:** General Discussion
**Created:** [January 16, 2022, 2:32pm UTC](https://community.freefem.org/t/finding-the-maximum-of-a-function-on-the-mesh/1438 "2022-01-16T14:32:47Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![romaingrvl](https://avatars.discourse-cdn.com/v4/letter/r/58956e/32.png) [@romaingrvl](https://community.freefem.org/u/romaingrvl)
#### Post date: [January 16, 2022, 2:32pm UTC](https://community.freefem.org/t/finding-the-maximum-of-a-function-on-the-mesh/1438/1 "2022-01-16T14:32:47Z")

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Hello to all of you FreeFem users,

After solving my system of PDE, I would like to compute the maximum value of my solution and the corresponding coordinates in my domain.

I found on another thread that I can do “u[].max” to find the maximum on the mesh (where u is my solution) but then how can I find the corresponding (x,y) coordinates ?

I know that the result of this procedure won’t be the true maximum if I use P2 elements because it gives the maximum value on vertices of the mesh but since I’m using a fine mesh it’s not really important, I don’t need a huge precision.

Thank you in advance.

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<div class="post-metadata">

### Author: ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)
#### Post date: [January 16, 2022, 2:45pm UTC](https://community.freefem.org/t/finding-the-maximum-of-a-function-on-the-mesh/1438/2 "2022-01-16T14:45:25Z")

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```auto
mesh Th = square(20, 20, [x+0.2,y+0.2]);
fespace Vh(Th, P2);
Vh u = cos(6*pi*x)*tanh(y) + sin(2*pi*y)*tanh(x);
plot(u);
int i = u[].imax;
cout << i << " " << u[](i) << " " << u[].max << endl;
Vh cx = x, cy = y;
cout << cx[](i) << " " << cy[](i) << endl;

```