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