Numerical simulation of atmospheric electricity problem with unknown ionosphere potential

The paper considers approaches to the numerical solution of the problem of the distribution of the electric potential in the framework of a two-dimensional model of the atmospheric section of the global electrical circuit. For this model, a nonstandard stationary elliptic boundary value problem with a nonclassical boundary condition is formulated. For the numerical solution of this problem, in order to study the possibility and efficiency of parallelization of calculations, two numerical algorithms based on the finite element method are used. The results of calculations for a model problem are presented, in which the features of the earth's surface topography are not taken into account, a simple model of conductivity and currents is used.