On Convergence of Support Operator Method Schemes for Differential Rotational Operations on Tetrahedral Meshes Applied to Magnetohydrodynamic Problems

The problem of constructing and justifying the discrete algorithms support operator method for numerical modeling differential repeated rotational operations vector analysis (curlcurl) in application to problems magnetohydrodynamics is considered. Difference schemes on unstructured meshes do not approximate equations local sense. Therefore, it necessary prove convergence these exact solution, which possible after analyzing error structure their approximation. For this analysis, a decomposition space mesh functions into an orthogonal direct sum subspaces potential vortex fields introduced. Generalized centroid-tensor metric representations tensor (div, grad, curl) are constructed. Representations have flux-circulation properties that integrally consistent spatial irregular structure. On smooth solutions model magnetostatic tetrahedral with first order accuracy rms sense, constructed difference proved. work can be used solve physical discontinuous magnetic viscosity, dielectric permittivity, or thermal resistance medium.