Abstract
A finite element formulation of full Maxwell's equations in terms of a vector potential and a scalar potential is presented. The vector potential and the scalar potential are approximated by novel vector basis functions and usual scalar basis functions, respectively. The linear equation finally obtained in this formulation always becomes singular, and then it can be solved only when both the given electric current and the given electric charge satisfy the equation of continuity. It is found that a gauge fixing of the potentials is transformed into regularization of the indeterminate linear equation. Two convenient gauge conditions for solving electromagnetic problems, magnetostatic problems and eddy current problems are proposed. These are the gauge of φ=0 and the extended Coulomb gauge.
