We consider a weighted least squares finite element approach to solving convection-dominated elliptic partial differential equations, which are difficult to approximate numerically due to the formation of boundary layers. The new approach uses adaptive mesh refinement in conjunction with an iterative process that adaptively adjusts the least squares functional norm. Numerical results show improved convergence of our strategy over a standard nonweighted approach. We also apply our strategy to the steady Navier–Stokes equations.
"Multiscale adaptively weighted least squares finite element methods for convection-dominated PDEs." Involve 5 (1) 39 - 49, 2012. https://doi.org/10.2140/involve.2012.5.39