# Implementing a non-constant stabilized parameter

**URL:** <https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869>\
**Category:** General Discussion\
**Created:** [July 3, 2022, 12:54am UTC](https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869 "2022-07-03T00:54:12Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![ramrebol](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/ramrebol/32/1227_2.png) [@ramrebol](https://community.freefem.org/u/ramrebol)\
**Post date:** [July 3, 2022, 12:54am UTC](https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869/1 "2022-07-03T00:54:12Z")

</div>

Hello. I’m starting with FreeFem, so sorry if my question is too simple, or if this is not the right place to ask something like this. But I haven’t found the answer in the tutorials.

I’m implementing a code to solve the Stokes Problem with velocity and pressure in P1 (space of continuous functions in the domain. Each element of the space is a linear polynomial in each element of the mesh). The mesh is the typical 2D mesh composed of triangles.

I short, the numerical scheme to solve the Stokes problem is:

```
solve Stokes( [u1, u2, p], [v1, v2, q] ) //, solver=LU)
= int2d(Th)(
 something + hK*something
	)
- int2d(Th)(
    somethign + hK*something
	)
+ on(1,2,3,4, u1=g1, u2=g2);

```

where

```
hK=4*AreaT/(3*r)

```

with AreaT is the area of the current triangle and

```
r = sqrt((x1-xc)^2+(x2-xc)^2+(x3-xc)^2+(y1-yc)^2+(y2-yc)^2+(y3-yc)^2)

```

where (x1,y1), (x2,y2), and (x3,y3) are the vertices of the current element (triangle) of the mesh, and

```
(xc,yc) = (x1+x2+x3,y1+y2+y3)/3.

```

Since each hK is different on each element, I don’t know how I could implement this stabilization parameter in the integral. In particular, how can I calculate “r”? Maybe it is not possible, and that is why I did not find a way to implement it.

Thanks in advance for your help and advice.

---

<div class="post-metadata">

**Author:** ![ramrebol](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/ramrebol/32/1227_2.png) [@ramrebol](https://community.freefem.org/u/ramrebol)\
**Post date:** [July 7, 2022, 10:25pm UTC](https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869/2 "2022-07-07T22:25:00Z")

</div>

Isn’t that a good question? Or maybe it’s not the place to ask it?

Maybe I wasn’t clear enough. Because I doubt FreeFem doesn’t have the option.

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**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [July 23, 2022, 8:23pm UTC](https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869/3 "2022-07-23T20:23:20Z")

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No problem , AreaT is defined in FreeFEM it is area.

Now computation of r

```auto
fespce Ph(Th,P0); // function constant par element
Ph xc=x,yc=x; // Barycenter of all element 
varf vr(unused,v) = int2d(Th,qft=qf1pTlump) ( 3*((x-xc)^2+(y-yc)^2)/area); 
Ph r;
r []= vr(0,Ph); 
r = sqrt(r); 

```

I am sorry the technics is tricking : qf1pTlump quadrature sum on all vertices of triangle /3  
and xc and yc is the barycenter of the triangle because the dof of Ph are all barycenter of triangle.

Remark: not tester so a bug is possible.

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<div class="post-metadata">

**Author:** ![ramrebol](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/ramrebol/32/1227_2.png) [@ramrebol](https://community.freefem.org/u/ramrebol)\
**Post date:** [July 27, 2022, 4:09pm UTC](https://community.freefem.org/t/implementing-a-non-constant-stabilized-parameter/1869/4 "2022-07-27T16:09:29Z")

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Many thanks prof. Hecht!!