Pavel Bochev, James Lai and Luke Olson A non-conforming least-squares finite element method for incompressible fluid flow problems International Journal for Numerical Methods in Fluids 72
We formulate and study numerically a new locally conservative least-squares FEM for the velocity–vorticity–pressure Stokes system, which uses a piecewise divergence-free basis for the velocity and standard C0 elements for the vorticity and pressure. The method achieves nearly perfect conservation of mass on a series of challenging test problems. Numerical results show excellent agreement with benchmark lid-driven cavity results. We also propose a simple diagonal pre-conditioner for the dV–VP formulation, which significantly reduces the condition number of the least-squares FEM problem.
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