Convergence of stabilized p1 finite element scheme for time harmonic maxwell’s equations

The paper considers the convergence study of the stabilized P1 finite element method for the time harmonic Maxwell’s equations. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. Our numerical examples validate obtained convergence results