## 6 Conclusions  
In this work, we presented a procedure for determining numerical values at the location of a measuring point when the actual position of the measuring point does not coincide exactly with one of the nodes of the finite element mesh. The proposed procedure is simple, efficient, and straightforward to implement:  
* The initial step is the determination of the element in which the measuring point is located and calculating the local coordinates of the measuring point within the element.
* Numerical values at the measuring points are then calculated through interpolation using the local coordinates and numerical values at the nodes of the element.  
The main motivation behind this work is to increase the robustness and adaptability of the Dam Monitoring System featuring the Finite Element Method software. This procedure can be utilized when additional instrument locations are added to the monitored system at a later time, allowing for the avoidance of remeshing of the numerical model. This procedure is applied to a dam structure, where potential and temperature are monitored through piezometers and thermometers, but it may be also be applied for other geomechanics problems, as well as engineering models in general. This algorithm can be particularly useful for academic, open source, and FEM solvers with narrow specialization, which lack the funding and development resources of commercial FEM solvers.  
The results demonstrated that, following calibration, the numerically calculated values of potential/temperature with the new interpolation algorithm better matched the measured values, not significantly, but nevertheless, with noticeable improvement, which varies from measuring point to measuring point, with the average relative difference for pore pressure reduced from 8.89% to 8.10%. The procedure also reveals that the calibra  
Figure 16: Potential field: (**a**) 2D cross section; (**b**) cut section in 3D model.  
tion procedure leads to the estimation of correct material properties which give accurate predictions of the potential and temperature validated by measured values.  
Overall, the proposed procedure is simple yet effective. The modified finite element solvers, which can be altered by users and integrated into other software, greatly improve dam safety monitoring systems through enhanced data analysis and prediction capabilities, based on well-calibrated material properties and detailed, realistic finite element geometry. While commercial solvers can serve as a point of comparison and model validation, they cannot be modified by users or integrated into other software such are Dam Monitoring Systems.  
Conceptualization, S.V. and M.Z.; methodology, S.V.; software, S.V.; validation, S.V., M.T. and V.M.; formal analysis, M.T. and D.D.; investigation, S.V. and V.M.; resources, S.V.; data curation, D.D.; writing--original draft preparation, S.V.; writing--review and editing, S.V. and M.T.; visualization, S.V. and V.M.; supervision, M.Z.; project administration, M.Z.; funding acquisition, D.D. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Science Fund of the Republic of Serbia, #GRANT No 7475, Prediction of damage evolution in engineering structures--PROMINENT; by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, contract No. 451-03-66/2024-03/200378; and by the Jaroslav Cerni Water Institute, Belgrade, Serbia, contract No. 32/22/30-03/07, Development of integral FEM model of HPP \"Djerdap 1\" dam.  
The original contributions presented in the study are included in the article material; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.