Pointwise Error Estimate for Spectral Galerkin Approximations of Micropolar Equations

On the convergence rate of Galerkin approximations for the magnetohydrodynamic type equations

“…Making use of this result, Rautmann ([18], [19]) proved the convergence rate in the ∥ • ∥ H 2 (Ω) -norm of the spectral Galerkin approximation of the solution without any compatibility condition. These results were extended to the finite element discretization of the Navier-Stokes equations by Bause [1], and to other systems of fluid mechanics by Boldrini et al (see [3]), and Climent-Ezquerra et al (see [6]).…”

Exponential stability for magneto-micropolar fluids

“…The second one, Theorem 5, is a L α result, α > 3, which is proved using energy estimates, using arguments from [2,3,22,32,19]. (3), and suppose either the initial data (u 0 , w 0 , h 0 ) ∈ H × L 2 (Ω ) × H and (f , g) ∈ H × L 2 (Ω ) to be sufficiently small or the viscosities µ, ν, ν 2 to be sufficiently large in such a way to assure uniqueness of the solution (v, z, b) for the stationary problem (5). There exist constants C > 0 and M > 0, independent of t, such that…”

“…In [17], the existence of restricted global attractors was showed through a semigroup approach. In [5], pointwise time error estimates in suitable Hilbert spaces were shown by considering spectral Galerkin approximations for strong solutions of the micropolar fluid model.…”

A decoupling finite element method with different time steps for the micropolar fluid model

“…For the spectral Galerkin approach of a spatial semi-discretization of the micropolar fluid model, Boldrini and Rojas-Medar [4] have studied the convergence rate of approximate solutions. Further, they have obtained a pointwise convergence rate without any compatibility conditions for the initial data [3]. A decoupled time-stepping finite element scheme for the evolutionary micropolar fluid flow model has been proposed and studied in [31], where the Navier-Stokes equations and the microrotational velocity equations are solved separately in each time step without iteration.…”