Unconditional stability and convergence analysis of fully discrete stabilized finite volume method for the time-dependent incompressible MHD flow

In this paper, we consider the stability and convergence of fully discrete stabilized finite volume method for unsteady incompressible magnetohydrodynamics (MHD) equations on quasi-uniform regular triangulations. The spatial discretization is based lowest equal-order mixed element pair velocity, pressure magnetic fields, while time backward Euler semi-implicit scheme. order to overcome restriction inf-sup condition, local projection employed. This has advantages parameter-free, no need calculate high-order derivatives or edge-based data structures it can be implemented at level. unconditional numerical scheme established by using Gronwall lemma, mathematical induction choosing different test functions. Optimal error estimates approximations in various norms are also presented constructing corresponding dual problem. Finally, some results proposed verify theoretical findings show performances considered method.