A Comparative Study of Finite Element and Finite Difference Methods for Cauchy-Riemann Type Equations
George J. Fix, Milton E. Rose · SIAM Journal on Numerical Analysis · 1985
A least squares formulation of the system ${\operatorname{div}}{\bf u} = \rho $, ${\operatorname{curl}}{\bf u} = \zeta $ is surveyed from the viewpoint of both finite element and finite difference methods. The latter employs box type differencing while the former is based on standard piecewise polynomial spaces. Closely related arguments are shown to establish convergence and stability.