  In order to perform electroencephalography (EEG) source reconstruction, i.e.,
to localize the sources underlying a measured EEG, the electric potential
distribution at the electrodes generated by a dipolar current source in the
brain has to be simulated, which is the so-called EEG forward problem. To solve
it accurately, it is necessary to apply numerical methods that are able to take
the individual geometry and conductivity distribution of the subject's head
into account. In this context, the finite element method (FEM) has shown high
numerical accuracy with the possibility to model complex geometries and
conductive features, e.g., white matter conductivity anisotropy. In this
article, we introduce and analyze the application of a discontinuous Galerkin
(DG) method, a finite element method that includes features of the finite
volume framework, to the EEG forward problem. The DG-FEM approach fulfills the
conservation property of electric charge also in the discrete case, making it
attractive for a variety of applications. Furthermore, as we show, this
approach can alleviate modeling inaccuracies that might occur in head
geometries when using classical FE methods, e.g., so-called "skull leakage
effects", which may occur in areas where the thickness of the skull is in the
range of the mesh resolution. Therefore, we derive a DG formulation of the FEM
subtraction approach for the EEG forward problem and present numerical results
that highlight the advantageous features and the potential benefits of the
proposed approach.
