We are interested here in materials presenting in some frequency range a dielectric permittivity with a small imaginary part and a negative real part. This occurs for instance for some metals (like silver) at optical frequencies. For such materials, very unsual singular phenomena take place at the corners, leading to numerical instabilities of finite elements. In particular, for some configurations, a part of the energy od surface plasmonic waves may be trapped by the corners: this is the so-called blackhole effect. In this presentation, we give a mathematical analysis of this blackhole phenomenon, based on a detailed description of the corner's sungularities, in the 2D case. Concerning numerical aspects, the treatment of corners of negative materials requires specific treatments. In configurations without blackhole effect, we show that the convergence of standard Finite Elements is ensured as soon as the mesh satisfies somes precise rules at the corners. But in presence of blackhole effect, this is not sufficient. The solution that we have found and validated is based on an original use of Pertfectly Matched Layers at the corners.