# The integral mesh and the mesh associated to test functions or unknown functions can be different in the case of varf form

**URL:** <https://community.freefem.org/t/the-integral-mesh-and-the-mesh-associated-to-test-functions-or-unknown-functions-can-be-different-in-the-case-of-varf-form/1103>\
**Category:** General Discussion\
**Created:** [July 19, 2021, 10:14am UTC](https://community.freefem.org/t/the-integral-mesh-and-the-mesh-associated-to-test-functions-or-unknown-functions-can-be-different-in-the-case-of-varf-form/1103 "2021-07-19T10:14:00Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![yongxing](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/yongxing/32/3632_2.png) [@yongxing](https://community.freefem.org/u/yongxing)\
**Post date:** [July 19, 2021, 10:14am UTC](https://community.freefem.org/t/the-integral-mesh-and-the-mesh-associated-to-test-functions-or-unknown-functions-can-be-different-in-the-case-of-varf-form/1103/1 "2021-07-19T10:14:00Z")

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Dear all,

I read from the FreeFem document (page 202, release 4.6) that " **The integral mesh and the mesh associated to test functions or unknown functions can be different in the case of**  
**varf form**". I am wondering what this means? for example, if we have two overlapped meshes Th and Ths, and

fespace Vh(Th, P1);  
Vh u, v;

fespace Vhs(Ths, P1);  
Vhs us;

varf a(u, v) = int2d(Th)( u\*v) + int2d(Ths)( u\*v)

**Would the above integral gives the following discretised form automatically:**

(A + P’ \* B \* P ) \* u = f

where **us = P\* u** with P is the interpolation matrix between mesh Th and Ths, A and B are discretised matrices from Th and Ths respectively?

Best,  
Yongxing.