Complementary solutions of electrostatic field problems

A general error form the corresponds to mismatch in the constitutive relationship is used for systematic derivation of complementary solution formulations, and the associated bounds, in electrostatic field problems. A close kinship between the error-based treatment and a general theorem on well-posed boundary conditions is made use of to highlight the role of boundary specifications in determining the expression for the complementary functionals. A combination of complementary computational results, obtained using two-dimensional finite elements is shown to provide valuable insight into numerical behavior.>