U-shaped seismic dampers, passive metallic devices that dissipate energy by cyclic plastic deformation, are designed to mitigate the effects of seismic loads on structures. This study focuses on the development of an advanced computational model of a U-shaped damper, chosen for its unique design of variable thickness and width, which contributes to its superior performance. The simulation uses nonlinear finite element analysis and a bilinear hardening model calibrated to the actual stress-strain curve of the low-carbon steel. To ensure accuracy, a rigorous mesh convergence analysis is performed to quantify numerical prediction errors and establish a model suitable for predicting local deformation phenomena, including strain and stress fields, throughout the displacement-based loading protocol. Mesh sensitivity analysis, performed by examining the equivalent stress and cumulative plastic strain, derives the damper hysteresis curve and confirms the convergence criteria of the mesh within the experimentally observed plastic response range of the material. The resulting computational model is a novel contribution that provides reliable predictions of local inhomogeneous deformation and energy dissipation, essential for optimizing damper design and performance through more sophisticated damage-fatigue models that guarantee the lifetime of a damper.