Convergence, error estimation and adaptivity in non-elliptic coupled electro-mechanical problems.

This paper presents the influence of the lack of ellipticity property on the solution convergence of the coupled electro-mechanical problems. This influence consists in the non-monotonic convergence which can hardly be described analytically. We recall our previous unpublished research where we demonstrate that the non-monotonicity depends very much on the energy level of the two component parts of the energy related to the coupled fields of mechanical and electric character. We further investigate the influence of this non-monotonic character of the convergence on the error estimation via equilibrated residual method. We also assess the influence of such convergence on the three-step error-controlled adaptive algorithms. We indicate the methods of practical overcoming the mentioned problems related to the lack of ellipticity. [ABSTRACT FROM AUTHOR]