A stabilizer-free pressure-robust finite element method for the Stokes equations

In this paper, we introduce a new finite element method for solving the Stokes equations in primary velocity-pressure formulation using H(div) elements to approximate velocity. Like other methods with velocity discretized by conforming elements, our has advantages of an exact divergence-free field and pressure-robustness. However, most require stabilizers enforce weak continuity tangential direction. Some need tune penalty parameter some them do not. Our is stabilizer free although discontinuous fields are used. Optimal-order error estimates established corresponding numerical approximation various norms. Extensive investigations conducted test accuracy robustness confirm theory. The examples cover low- high-order approximations up degree four, 2D 3D cases.