# Error order problem in 3D micropolar fluid numerical simulation

**URL:** <https://community.freefem.org/t/error-order-problem-in-3d-micropolar-fluid-numerical-simulation/3968>\
**Category:** General Discussion\
**Created:** [June 13, 2025, 10:20am UTC](https://community.freefem.org/t/error-order-problem-in-3d-micropolar-fluid-numerical-simulation/3968 "2025-06-13T10:20:42Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![AKang](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@AKang](https://community.freefem.org/u/AKang)\
**Post date:** [June 13, 2025, 10:20am UTC](https://community.freefem.org/t/error-order-problem-in-3d-micropolar-fluid-numerical-simulation/3968/1 "2025-06-13T10:20:42Z")

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3D micropolar fluid numerical simulation is being carried out. Using the BDF2 format, the time step is equal to the square of the space step. It is found that the L2 error of the velocity and angular velocity is a stable second order and does not reach the third order. However, the H1 error can stabilize to the second order. What causes this?

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<div class="post-metadata">

**Author:** ![AKang](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@AKang](https://community.freefem.org/u/AKang)\
**Post date:** [June 13, 2025, 10:37am UTC](https://community.freefem.org/t/error-order-problem-in-3d-micropolar-fluid-numerical-simulation/3968/2 "2025-06-13T10:37:59Z")

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In the two-dimensional simulations, the expected convergence rate is achieved, with the velocity exhibiting third-order accuracy in the L^2 norm.