Analysis of a dynamic electro‐elastic problem

We study a dynamic problem for linearly electro‐elastic materials, permitting piezoelectric effects. As a theoretical result, we state and prove the existence of a unique solution to the problem by using arguments of semi‐linear evolutionary equations and semigroups of linear continuous operators. Then we introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, we derive an optimal order error estimate. Finally, we present some numerical results on a two‐dimensional test problem to illustrate the theoretical error estimate.