  In this work, we propose and analyse a weak Galerkin method for the
electrical impedance tomography based on a bounded variation regularization. We
use the complete electrode model as the forward system that is approximated by
a weak Galerkin method with lowest order. The error estimates are studied for
the forward problem, which are used to establish the convergence of this weak
Galerkin algorithm for the inverse problem. Numerical examples are presented to
verify the effectiveness and efficiency of the weak Galerkin algorithm for the
electrical impedance tomography.
