Quantifying facility performance during thermophysical property measurement of liquid Zr using Electrostatic Levitation

The Hm-conforming virtual elements of any degree k on any shape of polytope in Rn with m, n \geq 1 and k \geq m are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case k = m, the set of degrees of freedom only involves function values and derivatives up to order m -1 at the vertices of the polytope. The inverse inequality and several norm equivalences for the Hm-conforming virtual elements are rigorously proved. The Hm-conforming virtual elements are then applied to discretize a polyharmonic equation with a lower -order term. With the help of the interpolation error estimate and norm equivalences, the optimal error estimates are derived for the Hm-conforming virtual element method.