Optimization of Anti Diffusion Fluxes in Difference Schemes for the Transport Equation

摘要

For numerical solving the transport equation the adaptive difference scheme is considered, which is constructed by means of addition of anti diffusion terms to the monotone difference scheme of the first order. The problem of finding anti diffusion fluxes is reduced to solving an optimization problem. The quality functional is chosen taking into account the increasing accuracy of the adaptive scheme and nonadmission of oscillations of the difference solution. The single valued solvability of the direct and conjugate finite-difference problems is proved. Differential properties of the quality functional are investigated and the necessary conditions of the optimality of the first order are obtained.