Finite element methods have been shown to achieve high accuracies innumerically solving the EEG forward problem and they enable the realisticmodeling of complex geometries and important conductive features such asanisotropic conductivities. To date, most of the presented approaches rely onthe same underlying formulation, the continuous Galerkin (CG)-FEM. In thisarticle, a novel approach to solve the EEG forward problem based on a mixedfinite element method (Mixed-FEM) is introduced. To obtain the Mixed-FEMformulation, the electric current is introduced as an additional unknownbesides the electric potential. As a consequence of this derivation, theMixed-FEM is, by construction, current preserving, in contrast to the CG-FEM.Consequently, a higher simulation accuracy can be achieved in certainscenarios, e.g., when the diameter of thin insulating structures, such as theskull, is in the range of the mesh resolution. A theoretical derivation of the Mixed-FEM approach for EEG forwardsimulations is presented, and the algorithms implemented for solving theresulting equation systems are described. Subsequently, first evaluations inboth sphere and realistic head models are presented, and the results arecompared to previously introduced CG-FEM approaches. Additional visualizationsare shown to illustrate the current preserving property of the Mixed-FEM. Based on these results, it is concluded that the newly presented Mixed-FEMcan at least complement and in some scenarios even outperform the establishedCG-FEM approaches, which motivates a further evaluation of the Mixed-FEM forapplications in bioelectromagnetism.
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