О сходимости разностных схем метода опорных операторов для ротационных операций векторного анализа на тетраэдрических сетках

Abstract

One approach to the description of the metric properties of an irregular grid is proposed for discretizing repeated rotational operations of vector analysis (rot rot) as applied to modeling the magnetic and electric fields. On the basis of the support operator method and the used grid metric, integrally consistent vector analysis operations rot, div, grad are constructed that are necessary to obtain convergence estimates for difference schemes for repeated rotational operations, as well as solving physical problems with discontinuous magnetic viscosity, dielectric permeability or thermal resistance of a medium. On smooth solutions of the model magnetostatic problem on a tetrahedral grid with first order of accuracy in the mean-square sense, the convergence of the constructed difference schemes with zero eigenvalue of the spectral problem is proved. At the same time, no restrictions are imposed on an irregular tetrahedral mesh, except for its non-degeneracy.