Properties of grid boundary value problems for functions defined on grid cells and faces

Properties of a version of MFD method are studied for a grid problem on a polyhedral grid in which the grid scalars are defined on grid cells and the grid flows are specified by their local normal coordinates on the plane faces of cells. In a domain with curvilinear boundary, a grid inhomogeneous boundary value problem for stationary diffusion-type equations is considered. An operator statement of the grid problem is given, and a local approximation of the equations and boundary conditions is studied.