A fully discrete finite element scheme for the Kelvin-Voigt model

Abstract

In this paper, we study convergence of a fully discrete scheme for the two-dimensional nonstationary Kelvin-Voigt model. This scheme is based on a finite element approximation for space discretization and the Crank-Nicolson-type scheme for time discretization, which is a two step method. Moreover, we obtain error estimates of velocity and pressure. At last, the applicability and effectiveness of the present algorithm are illustrated by numerical experiments.

Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows

“…Taking v h = 1 2 (ξ 1 h + ξ 0 h ) and r h = 1 2 (ψ 1 h + ψ 0 h ), the trilinear terms on the RHS of (43)-(46) can be treated exactly as in ( 21) and (29). This leads to the upper bound…”

“…The MHD-Voigt regularization model is derived from MHD model by adding a Voigt regularization term to each of the momentum and magnetic field equations. Recently, a number of research works have focused on the Voigt-type regularizations in the context of various hydrodynamic models, see, e.g., [7,10,18,19,22,26,33,28,29]. An important aspect of the MHD-Voigt model is that when used as a regularization for the MHD equations the regularization is inviscid, which means it does not add artificial viscosity.…”