A full divergence-free of high order virtual finite element method to
approximation of stationary inductionless magnetohydrodynamic equations on
polygonal meshes
In this present paper we consider a full divergence-free of high order
virtual finite element algorithm to approximate the stationary inductionless
magnetohydrodynamic model on polygonal meshes. More precisely, we choice
appropriate virtual spaces and necessary degrees of freedom for velocity and
current density to guarantee that their final discrete formats are both
pointwise divergence-free. Moreover, we hope to achieve higher approximation
accuracy at higher "polynomial" orders k_{1} \geq 2, k_{2} \geq 1, while the
full divergence-free property has always been satisfied. And then we processed
rigorous error analysis to show that the proposed method is stable and
convergent. Several numerical tests are presented, confirming the theoretical
predictions