  The goal of this study is to develop focal, accurate and robust finite
element method (FEM) based approaches which can predict the electric potential
on the surface of the computational domain given its structure and internal
primary source current distribution. While conducting an EEG evaluation, the
placement of source currents to the geometrically complex grey matter
compartment is a challenging but necessary task to avoid forward errors
attributable to tissue conductivity jumps. Here, this task is approached via a
mathematically rigorous formulation, in which the current field is modeled via
divergence conforming H(div) basis functions. Both linear and quadratic
functions are used while the potential field is discretized via the standard
linear Lagrangian (nodal) basis. The resulting model includes dipolar sources
which are interpolated into a random set of positions and orientations
utilizing two alternative approaches: the position based optimization (PBO) and
the mean position/orientation (MPO) method. These results demonstrate that the
present dipolar approach can reach or even surpass, at least in some respects,
the accuracy of two classical reference methods, the partial integration (PI)
and St. Venant (SV) approach which utilize monopolar loads instead of dipolar
currents.
