Publication Date:
2018-03-06
Description:
We present a convergence analysis for the space discretization via a dual-mixed formulation of a time-dependent system of partial differential equations modeling an elastoacoustic interaction problem. The resulting unknowns are given by the stress tensor in the solid and the pressure in the fluid, so that the Arnold–Falk–Winther mixed finite element method with weak symmetry in the structure and the usual Lagrange finite element method in the acoustic medium are employed to define the associated semidiscretization. We analyse the resulting global semidiscrete scheme by introducing here for the first time an adequate projector and its discrete counterpart and by estimating the error between them. We show that the method is stable uniformly with respect to the space discretization parameter and the Poisson modulus, and derive the corresponding asymptotic error estimates. In addition, our approach allows the postprocessing of the displacement and the velocity with analog convergence results.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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