Fully discrete finite element schemes for the nonstationary 3D magneto-micropolar equations

03/10/2023
by   Hailong Qiu, et al.
0

In this paper we consider three kinds of fully discrete time-stepping schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some magnetic field. The first scheme is comprised of the Euler semi-implicit discretization in time and conforming finite element/stabilized finite element in space. The second one is based on Crank-Nicolson discretization in time and extrapolated treatment of the nonlinear terms such that skew-symmetry properties are retained. We prove that the proposed schemes are unconditionally energy stable. Some optimal error estimates for the velocity field, the magnetic field, the micro-rotation field and the fluid pressure are obtained. Furthermore, we establish some fully discrete first-order decoupled time-stepping algorithms. Numerical tests are provided to check the theoretical rates and unconditionally energy stable.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset