# New finite element with dependence on neighbours

**URL:** https://community.freefem.org/t/new-finite-element-with-dependence-on-neighbours/3653
**Category:** General Discussion
**Created:** [December 19, 2024, 10:10am UTC](https://community.freefem.org/t/new-finite-element-with-dependence-on-neighbours/3653 "2024-12-19T10:10:23Z")
**Posts on this page:** 1
**Showing post:** 3

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### Author: ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [January 9, 2025, 9:03am UTC](https://community.freefem.org/t/new-finite-element-with-dependence-on-neighbours/3653/3 "2025-01-09T09:03:35Z")

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Dear Frédéric,  
Thank you for your answer. Upon your advice, I have found a bypass, by using the fact that my space is a subspace of a known fespace on the split mesh Ths=splitmesh6PowellSabin(Th0).  
I have performed a “space reduction” similar to what is done with on(tgv=-1): I replaced some well chosen lines in my matrix by constraints defining the subspace.

Nevertheless I would be interested in learning to define fespaces, and understanding the meaning of all the parameters involved. Probably other users would be interested also (for example [What does the array of ``data[]'' represent during the process of adding a new finite element?](https://community.freefem.org/t/what-does-the-array-of-data-represent-during-the-process-of-adding-a-new-finite-element/3635) ). I don’t think there is a tuto on that.

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