Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Abstract

Abstract Mathematical physics problems are often formulated by means of the vector analysis differential operators: divergence, gradient and rotor. For approximate solutions of such problems it is natural to use the corresponding operator statements for the grid problems, i.e., to use the so-called VAGO (Vector Analys Grid Operators) method. In this paper, we discuss the possibilities of such an approach in using gen- eral irregular grids. The vector analysis di®erence operators are constructed using the Delaunay triangulation and the Voronoi diagrams. The truncation error and the consistency property of the di®erence operators constructed on two types of grids are investigated. Construction and analysis of the di®erence schemes of the VAGO method for applied problems are illustrated by the examples of stationary and non-stationary convection-diffusion problems. The other examples concerned the solution of the non- stationary vector problems described by the second-order equations or the systems of first-order equations.