In this thesis, time-harmonic Maxwell's equations are our main interest,in order to compute accurately the radar cross section of electromagnetic targets.To have a good precision in large-scale experiments, higher-order finite element methods are used.In the scalar case, hexahedral spectral finite element, with mass lumping,provide a fast matrix-vector product with a low storage.In the vectorial case, Nedelec's first family hexahedral elementdoesn't lead to mass lumping, but a fast matrix-vector can be found.Numerical results in 3-D show the efficiency of this algorithm.The case, where the geometry is invariant under rotation, is treated.This symmetry leads to solve a sequence of 2-D independent problems.A higher-order finite element method is proposed. This methodis coupled with higher-order boundary element method.
