  This paper constructs and analyzes a boundary correction finite element
method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher
splits. The velocity space consists of continuous piecewise quadratic
polynomials, and the pressure space consists of piecewise linear polynomials
without continuity constraints. A Lagrange multiplier space that consists of
continuous piecewise quadratic polynomials with respect to boundary partition
is introduced to enforce boundary conditions as well as to mitigate the lack of
pressure-robustness. We prove several inf-sup conditions, leading to the
well-posedness of the method. In addition, we show that the method converges
with optimal order and the velocity approximation is divergence free.
