The Stability Condition and Energy Estimate for Non-stationary Problems of Coupled Electroelasticity

In this paper a coupled problem of dynamic electroelasticity is investigated using the variational approach and the concept of generalized solutions. We derive a numerical procedure directly from the deenition of the generalized solution of the problem. We prove the convergence of the numerical scheme (with the second order in space-time) to the solution of the original problem from a class of generalized solutions. The stability condition is obtained from an energy estimate. It is shown that such a condition is the Courant-Friederichs-Lewy-type stability condition, being dependent on the velocity of mixed electro-elastic waves. Coupling eeects are discussed with a numerical example.gence and stability.