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 least-squares method has. However, one of the 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 the least-squares method minimizes the continuity equation in $L^2$-norm. In this paper, we explore the reason for the mass loss and provide new approaches to retain the mass even in a severely underresolved grid.