On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the individual...