The Finite Element Analysis of the Controlled-Source Electromagnetic Induction Problems by Fractional-Step Projection Method

Abstract

This paper provides a convergence analysis of a fractional-step projection method for the controlled-source electromagnetic induction problems in heterogenous electrically conduting media by means of finite element approximations. Error estimates in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $\mathcal{O}(h^s+\tau)$) in the $L^2$-norm for the magnetic field $\boldsymbol{H},$ where $h$ is the mesh size and $1/2 < s ≤ 1$.