This study explores the design and simulation of two graphene-based terahertz (THz) absorbers using the finite element method (FEM). The first model operates in the mid-infrared range (6 to 14 μm) and is suitable for applications such as thermal imaging, remote sensing, and spectroscopy. The second model operates in the far-infrared range (1 to 14 THz) and is versatile for spectroscopy, imaging, communication, and sensing. Key contributions include a meta-atom with the smallest footprint, a practical absorber design, and tunability through the chemical potential of the graphene layer. Numerical analysis and simulations demonstrate effective absorption, and sensitivity analysis shows the impact of analyte refractive index and thickness on sensing performance. Model 2, focusing on tunable graphene absorbers, exhibits remarkable absorption characteristics, achieving tunable absorptivity from 3 to 99.5%. This research advances the field of tunable THz absorbers, showcasing potential in diverse applications, and opens new avenues for efficient and flexible terahertz technology.This study explores the design and simulation of two graphene-based terahertz (THz) absorbers using the finite element method (FEM). The first model operates in the mid-infrared range (6 to 14 μm) and is suitable for applications such as thermal imaging, remote sensing, and spectroscopy. The second model operates in the far-infrared range (1 to 14 THz) and is versatile for spectroscopy, imaging, communication, and sensing. Key contributions include a meta-atom with the smallest footprint, a practical absorber design, and tunability through the chemical potential of the graphene layer. Numerical analysis and simulations demonstrate effective absorption, and sensitivity analysis shows the impact of analyte refractive index and thickness on sensing performance. Model 2, focusing on tunable graphene absorbers, exhibits remarkable absorption characteristics, achieving tunable absorptivity from 3 to 99.5%. This research advances the field of tunable THz absorbers, showcasing potential in diverse applications, and opens new avenues for efficient and flexible terahertz technology.