Lithium-ion batteries are exposed to a variety of degradation effects which negatively impact their lifetime. Due to the small spatial scale of these effects and the electrochemical complexity of the batteries, experimental insights are limited. Thus, numerical simulations of physical models can yield valuable insights into the underlying processes, while also providing a supplementary tool for digital prototyping. In this thesis, a model of nonlinear partial differential equations is considered which describes the lithium-ion concentration and the electric potential within the spatially resolved microstructure of the battery. Furthermore, the model accounts for one of the major contributors to capacity fade: the solid electrolyte interphase (SEI). The thesis extends on a previous monolithic solver using a fully implicit finite volume formulation by investigating an alternative flux approximation scheme for the coupled transport inside the electrolyte and developing a novel semi-implicit solution scheme. This semi-implicit scheme addresses handling of the SEI model within the coupled formulation and shows a significant improvement in robustness and performance for the considered simulations.weiterlesen