The article analyzes the numerical solution for the electric field strength and the nanotriode emission current. The finite element method on an nonuniform mesh with the implementation of algorithms in Matlab is used. Discusses related issues of application of Matlab PDE Toolbox software package related to the specifics of modeling of autoemission systems: * computing the area of complex shapes includes a boundary of the emitter with a large surface curvature and small sizes, which leads to a significant variation of the characteristic sizes in the same geometric configuration; * exponential dependence of the current density on the field strength requires increased accuracy when taking into account the boundary conditions on the emitter