# Rate fo convergence for fourth-order variational inequality

**URL:** <https://community.freefem.org/t/rate-fo-convergence-for-fourth-order-variational-inequality/4097>\
**Category:** General Discussion\
**Created:** [October 8, 2025, 7:28am UTC](https://community.freefem.org/t/rate-fo-convergence-for-fourth-order-variational-inequality/4097 "2025-10-08T07:28:52Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![smail](https://avatars.discourse-cdn.com/v4/letter/s/cab0a1/32.png) [@smail](https://community.freefem.org/u/smail)\
**Post date:** [October 8, 2025, 7:28am UTC](https://community.freefem.org/t/rate-fo-convergence-for-fourth-order-variational-inequality/4097/1 "2025-10-08T07:28:52Z")

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Hi,

I’m trying to compute the order of convergence for a fourth-order variational inequality using the penalty method, in FreeFEM++. But I got unexpected results.  
I computed the L2 and the H1 errors against an exact solution, but the convergence rate seems to be inconsistent with the theoretical results. Note that the exact solution has H3 global regularity.

[Rate-VI-4.edp](https://community.freefem.org/uploads/short-url/xnPROdRL5bIyQDyDVl7zQUWSBxG.edp) (4.1 KB)

Attached here is the code that I have used.

Best regards.