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Analysis of a dynamic electro‐elastic problem
Journal article

Analysis of a dynamic electro‐elastic problem

M Barboteu, K Kazmi, M Sofonea and W Han
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol.93(9), pp.612-632
09/2013
DOI: 10.1002/zamm.201200113

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Abstract

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. The authors study a dynamic problem for linearly electro‐elastic materials, permitting piezoelectric effects. As a theoretical result, they 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 they introduce a fully discrete scheme to solve the problem numerically. Under certain solution regularity assumptions, the authors derive an optimal order error estimate. Finally, they present some numerical results on a two‐dimensional test problem to illustrate the theoretical error estimate.
 error estimation Piezoelectric material electro‐elastic constitutive law finite element method convergence infinitesimal generator C0 semigroup of linear continuous operators fully discrete scheme numerical simulation

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