We investigate low-frequency electromagnetic wave propagation and absorption properties in 2D and 3D plasma configurations. For these purposes, we have developed a new full-wave 3D code LEMan that determines a global solution of the wave equation in bounded stellarator plasmas excited with an external antenna. No assumption on the wavelength compared to the plasma size is made, all the effects of the 3D geometry and finite plasma extent are included. The equation is formulated in terms of electromagnetic potentials in order to avoid numerical pollution effects. The code utilises linear and Hermite cubic finite element discretisation in the radial direction and Fourier series in the poloidal and toroidal variables. The full cold plasma model including finite electron inertia and, thus, mode conversion effects is implemented. The code uses Boozer magnetic coordinates and has an interface to the TERPSICHORE code. Special care is taken to treat the magnetic axis and to ensure the unicity of the numerical solution. The discretisation, interpolation and numerical derivation methods specifically adapted for our problem avoid the energy sink in the origin and provide a very good local and global energy conservation. A special algorithm has been developed to analytically expand the wave equation coefficients in the full 3D stellarator geometry. The code has been specifically optimised for vector computing platform, reaching close to maximum average performances on the NEC SX5 machine. The code has been applied in 1D, 2D, and 3D geometries. No unphysical solutions have been observed. LEMan successfully recovers all the fundamental properties of the Alfvén spectrum (gaps, eigenmodes). Benchmarks have been made against the 2D LION code and JET experimental measurements, showing a good agreement between the results.