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.
Keywords
partial differential equations, finite element methods,
convection, boundary layers