GLEMuR (Gpu-based Lagrangian mimEtic Magnetic Relaxation) is a finite difference Lagrangian code which uses mimetic differential operators and runs on Nvidia GPUs. Its main purpose is to study the relaxation of magnetic relaxation in environments of zero resistivity and viscosity; it preserves the magnetic flux and the topology of magnetic field lines. The use of mimetic operators for the spatial derivatives improve accuracy for high distortions of the grid, and the final state of the simulation approximates a force-free state with a significantly higher accuracy. Note, however, that GLEMuR is not a general purpose equation solver and the full magnetohydrodynamics equations are not implemented.