Difference Schemes and the Analysis of Approximate Solutions for Two-dimensional Nonstationary Problems of Coupled Electroelasticity

Melnik (R.)V.N. and Moskalkov M.N.

Differential Equations, 27 (7), 860-867, 1991

Abstract:

Using the Faedo-Galerkin method the authors prove the existence and uniqueness of the generalized solution of the problem indicated in the title. By means of integral identities of the Faedo-Galerkin method, they construct an explicit difference scheme whose conditions for stability coincide with conditions for nonnegativity of the difference analogue of the total energy of an electromechanical system. Under additional conditions for smoothness of the solution of the problem they prove the convergence of the difference scheme.