Enhanced Mass Conservation in Least-Squares Methods for Navier-Stokes Equations

There are many applications of the least-squares finite element method for the numerical solution of partial differential equations because of a number of benefits that the leastsquares method has. However, one of most well-known drawbacks of the least-squares finite element method is the lack of exact discrete mass conservation, in some contexts, due to the fact that leastsquares method minimizes the continuity equation in L norm. In this paper, we explore the reason of the mass loss and provide new approaches to retain the mass even in severely under-resolved grid.