Exponential finite volume schemes for solving of evolutional equations on irregular grids

A numerical solution of evolutionary equations on irregular grids is considered. The conservative weakly monotone finite volume schemes on both triangular and tetrahedral grids for convection-diffusion type equations are proposed. The conditions of stability and convergence of these schemes are formulated. The proposed numerical approach are illustrated for one vacuum microelectronics problem connected with computations of electron emission from edge surface of silicon microcathode.