Computational aspects of finite volume methods (Q1571294)

This paper is devoted to the technical issues that arise in solving two-dimensional elliptic and three-dimensional mixed boundary value problems with piecewise-smooth coefficients by finite volume methods. Two families of difference approximations on various types of mesh patterns are suggested. The concepts of local balance matrix and global matrix of the system of linear algebraic equations are introduced that are similar to the concepts of the local and global stiffness matrix used in the finite element method. Error estimates of the numerical solution are given.