ERROR ESTIMATION FOR A PIEZOELECTRIC CONTACT PROBLEM WITH WEAR AND LONG MEMORY

We study a mathematical model for a quasistatic behavior of electro-viscoelastic materials. The problem is related to highly nonlinear and non-smooth phenomena like contact, friction and normal compliance with wear. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. For a numerical scheme, we prove the existence and uniqueness of the solutions, and derive optimal order error estimates under certain regularity assumption on the solution of the continuous problem. AMS subject classification. 35J85 · 49J40 · 47J20 · 74M15. REFERENCES [1] Aoun, M. S. M., Dehda, B., & Douib, B. (2024). Numerical study of a thermo-elasto-viscoplastic contact problem with adhesion using a hybrid method. Studies in Engineering and Exact Sciences, 5(2), e8308-e8308. Search in Google Scholar. https://doi.org/10.54021/seesv5n2-255 [2] Aoun, M. S. M., Selmani, M., & Ahmed, A. A. 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Analysis and numerical solution of a piezoelectric frictional contact problem. Applied mathematical modelling, 36(9), 4483-4501. Search in Google Scholar. https://doi.org/10.1016/j.apm.2011.11.077 Communicated Editor: T.J. RABEHERIMANAN Manuscript received Sep. 19, 2024; revised Feb 02, 2025; accepted Feb 11, 2025; published Feb 28, 2025.