# Ciarlet-Raviart for Biharmonic equation, Underconstrained system

**URL:** <https://community.freefem.org/t/ciarlet-raviart-for-biharmonic-equation-underconstrained-system/2582>\
**Category:** General Discussion\
**Created:** [July 5, 2023, 11:09am UTC](https://community.freefem.org/t/ciarlet-raviart-for-biharmonic-equation-underconstrained-system/2582 "2023-07-05T11:09:09Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![tomgilat](https://avatars.discourse-cdn.com/v4/letter/t/a9a28c/32.png) [@tomgilat](https://community.freefem.org/u/tomgilat)\
**Post date:** [July 5, 2023, 11:09am UTC](https://community.freefem.org/t/ciarlet-raviart-for-biharmonic-equation-underconstrained-system/2582/1 "2023-07-05T11:09:09Z")

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Hi there. I am using FreeFEM++ to solve a biharmonic equation using Ciarlet-Raviart formulation. I want to know what happens if “solve” has an underconstrained system?

I am asking because I disregard the fact that one of the test functions should be in H^1\_0, and I am not getting what I am expecting. The formulation also has two equalities and I provide them as a single one to “solve”.

I will really appreciate your help.  
Tom

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**Author:** ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)\
**Post date:** [July 5, 2023, 12:23pm UTC](https://community.freefem.org/t/ciarlet-raviart-for-biharmonic-equation-underconstrained-system/2582/2 "2023-07-05T12:23:06Z")

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I guess you could post your code but if you are looking into this anyway it  
may help to just write out the weak formulation and see what happens.  
You can formulate a simple problem on a small square grid mesh  
with a FF “varf” and dump the matrix and rhs and  
see if it makes sense.