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Analysis of a dynamic electro‐elastic problem
Author(s) -
Barboteu M.,
Kazmi K.,
Sofonea M.,
Han W.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200113
Subject(s) - mathematics , scheme (mathematics) , dynamic problem , order (exchange) , mathematical optimization , linear elasticity , state (computer science) , computer science , mathematical analysis , algorithm , finite element method , physics , thermodynamics , finance , economics
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.