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Belaid L’kaihal, El Hassan Essoufi, Mustapha Bouallala, Solvability and numerical approximation of a dynamic frictionless thermo-viscoelastic contact problem

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DOI: 10.23952/jano.8.2026.3.02
Volume 8, Issue 3, 1 December 2026, Pages 337-354

 

Abstract. In this paper, we investigate a dynamic contact problem involving a thermo-viscoelastic body in interaction with a thermally conductive foundation. The contact is modeled by using the normal compliance condition, which allows for a realistic description of the contact mechanics. We rigorously establish existence and uniqueness results for a weak solution of the problem by applying the Banach fixed-point theorem. Furthermore, we introduce a fully discrete approximation based on the finite element method combined with a backward Euler time-stepping scheme. Detailed error estimates are then derived, leading to a linear convergence rate under suitable additional regularity assumptions on the solution and the problem data.

 

How to Cite this Article:
B. L’kaihal, E.H. Essoufi, M. Bouallala, Solvability and numerical approximation of a dynamic frictionless thermo-viscoelastic contact problem, J. Appl. Numer. Optim. 8 (2026), 337-354.