Astrocytes, a crucial glial cell type in the brain, play a vital role in maintaining ion and energy homeostasis while actively participating in neuronal information processing and memory formation. Calcium is considered the main readout signal of astrocytes. Several studies have shown a significant heterogeneity in morphology within brain regions like the hippocampus. To enhance our understanding of the morphology and function of cells, computational models can aid experiments. Oschmann et al. proposed a computational model integrating two glutamate pathways triggering calcium elevations: activation of metabotropic glutamate receptors (mGluRs) and glutamate transporters (EAATs) at the plasma membrane. The mGluR pathway involves extracellular glutamate binding, leading to calcium release from the endoplasmic reticulum through inositol 1,4,5-trisphosphate (IP3) receptor channels, initiating a calcium-induced calcium release. Simultaneously, the EAATs transport potassium out as well as sodium and glutamate in. The affected sodium-calcium exchanger conveys sodium and calcium ions, and the sodium-potassium-ATPase facilitates sodium outflux and potassium influx. We transformed the single-compartment model by Oschmann et al. into a finite element method (FEM) model, facilitating the study of ion and transmitter molecules at a fine spatiotemporal scale. Additionally, the FEM model was applied to five different astrocyte shapes to investigate the resulting ion dynamics. This integrated approach provides valuable insights into the complex interplay of astrocyte morphology and function.