Weighted-Norm First-Order System Least-Squares (FOSLS) for Div/Curl Systems with Three Dimensional Edge Singularities

A weighted-norm first-order system least-squares (FOSLS) method for div/curl problems with edge singularities is presented. Traditional finite element methods, including least-squares methods, often suffer from a global loss of accuracy due to the influence of a nonsmooth solution near polyhedral edges. By minimizing a modified least-squares functional, optimal accuracy in weighted and non-weighted norms is recovered. Error estimates with and without mesh refinements are presented and numerical results are given to confirm the theory.