This thesis focuses on a wellknown issue of discretization techniques for solving the incompressible Navier Stokes equations. Due to a weak treatment of the incompressibility constraint there are different disadvantages that appear, which can have a major impact on the convergence and physical behaviour of the solutions. First we approximate the equations with a wellknown pair of elements and introduce an operator that creates a reconstruction into a proper space to fix the mentioned problems. \newline Afterwards we use an H(div) conforming method that already handles the incompressibility constraint in a proper way. For a stable high order approximation an estimation for the saddlepoint structure of the Stokes equations is needed, known as the LadyschenskajaBabuskaBrezzi (LBB) condition. The independency of the estimation from the order of the polynomial degree is shown in this thesis. For that we introduce an H^2stable extension that preserves polynomials. All operators and schemes are implemented based on the finite element library Netgen/NGSolve and tested with proper examples.
