Mathematical modeling of the three-dimensional electromagnetic fields in the frequency domain for magnetotelluric flexings

In this paper, a vector variational formulation for a second order equation for the field $\mathbf{E}$ and a mixed vector variational formulation for a sistem of the Maxwell equations in the frequency domain are constructed. A mixed vector and a vector finite element analogues of variational formulations are obtained for edge- and face- basis functions. A computational scheme for modeling of the three-dimensional harmonic electromagnetic fields in composite areas, where each of subregions has different physical characteristics, based on the vector and the mixed vector finite element method is constructed and studied Numerical modeling of the three-dimensional quasi-stationary electromagnetic fields on a class of magnetotelluric problems is performed.