Convergence of the Operator-Difference Scheme to Generalized Solutions of Coupled Field Theory Problem

Melnik R.V.N.

Journal of Difference Equations and Applications, 4, 185--212, 1998

Abstract:

In this paper the operator-difference scheme for the numerical solution of a problem arising from coupled field theory is thoroughly investigated for the case when the classical assumptions of sufficient smoothness cannot be applied. Such a situation, being typical in many applications, is considered for the problem of nonstationary electroelasticity.

A new a-priori estimation for the numerical solution of the problem has been obtained. A scale of accuracy results for generalized solutions of the problem has been derived, and the convergence theorem has been proved. Applications of the theory are considered and computational results are discussed.