APro, developed in KAERI for the process-based total system performance assessment (TSPA) of deep geological disposal systems, performs finite element method (FEM)-based multiphysics analysis. In the FEM-based analysis, the mesh element quality influences the numerical solution accuracy, memory requirement, and computation time. Therefore, an appropriate mesh structure should be constructed before the mesh stability analysis to achieve an accurate and efficient process-based TSPA. A generic reference case of DECOVALEX-2023 Task F, which has been proposed for simulating stationary groundwater flow and time-dependent conservative transport of two tracers, was used in this study for mesh stability analysis. The relative differences in tracer concentration varying mesh structures were determined by comparing with the results for the finest mesh structure. For calculation efficiency, the memory requirements and computation time were compared. Based on the mesh stability analysis, an approach based on adaptive mesh refinement was developed to resolve the error in the early stage of the simulation time-period. It was observed that the relative difference in the tracer concentration significantly decreased with high calculation efficiency.