Zhdanova I. Mathematical simulation and control of diffusion and heat-mass exchange processes

In the thesis the numerical solution algorithms for unilateral processes models in form of variational inequalities are proposed. The algorithms are based on functional parametrization method and subgradient or approximation approach. Considered inequalities have nonsmooth functionals of accordance, or such ones that take infinite values. The scheme of finite-element models solution based on sections method is modified, that makes it possible to shorten requirements for memory. The algorithm of adaptive grid generation is proposed, it functionates in coordination with algorithm of reconstruction of unknown obstacle function or function of unilateral conductivity. The algorithm of control of processes with "hard" unilateral properties is proposed. The problem of simulation and control of oils filtration process with critical pressure gradient is solved. The program support for simulation of this unilateral process is developed.