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Abstract

In this thesis numerical methods for the solution process of the Newman-type lithium ion battery (LIB) model with a distribution of spherical particles with different radii are derived. Since the Newman-type LIB model is a multiscale model, where the scales cannot be completely separated, it has a pseudo twodimensional structure. To be solved it needs the solution of a so called cell problem. Furthermore, it consists of a homogenized and a microscopic part that have to be solved coupled. The solution process of the cell problem is done with the CutCell method to improve reconstruction properties of the microstructure. Therefore, the condition number of a Laplace problem with the CutCell method is investigated and it is shown that a simple preconditioner can improve the condition problems due to the CutCell method. Furthermore, a goal oriented a posteriori error estimator based on the dual weighted residual (DWR) method is derived for the CutCell method. For the LIB model the condition number is investigated and a simple preconditioner is suggested. Based on the DWR method a goal oriented error estimator is derived and tested for the pseudo twodimensional problem. The model behavior of this extension is investigated, especially the occurrence of the different deintercalation properties of the particles with different radii. Furthermore, a simplified model for small charge/discharge rates for an anode is derived and compared to the full model. In the end, the sensitivity of full Newman-type model with respect to two parameters, which are hard to determine experimentally, is investigated.