Divergence-free H(div) finite element method for stokes equation

Abstract

We wish to devise an efficient method to find the mass conserving solution to the Stokes problem, used widely in physics or fluid dynamics. Previously known numerical methods are based on using appropriate elements which satisfy inf-sup conditions for velocity and pressure. Such method creates a large saddle-point problem in solving the matrix equation by deteriorating the convergence. In order to overcome such challenge, we define a new form of finite dimension function space which satisfies Divergence-free condition which leads to a positive definite matrix system that improves the efficiency of the numerical procedure of solving the Stokes problem.