General Interpolation Formulas for Spaces of Discrete Functions with Nonuniform Meshes

Abstract

The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as the sum of powers of discrete values, the discrete maximum modulo, the discrete Hölder and Lipschitz coefficients.