A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning

This is the third part in a series on mass conserving, high order, mixed finite element method for 2D Stokes flow. In this part, we study block-diagonal preconditioner indefinite Schur complement system arising from discretization of equations using these elements. The underlying uniformly stable both mesh size $h$ and polynomial order $p$, prove bounds eigenvalues preconditioned which are independent grow modestly $p$. analysis relates to an appropriate variational setting with subspaces exact sequence properties inf-sup stability hold. Several numerical examples demonstrate agreement theoretical results.