A one-dimensional quasi-static contact problem in linear thermoelasticity

Abstract

The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.

Finite element approximation to a contact problem in linear thermoelasticity

“…In [4] Copetti and Elliott have also proposed and analysed a finite element approximation. The quasi-static problem with the body clamped at the boundary was studied by Day in [6].…”

“…It would be natural to consider the general case where the temperature at x = 0 is time dependent and may be different from the value of the initial temperature at x = 0. This was done by Copetti and Elliott in [4] when the temperature of the body is constant at both ends.…”

Boundary heat flux estimation in quasi-static thermoelastic systems

“…We show that if functions ω 1 and ω 2 are C 2 [0, 1] and not identical, while Ω ω i (ξ) dξ = 0, i = 1, 2, (without loss of generality, we assume that Ω ω i (ξ) dξ = 1), then the function u(t) is identifiable from the measurements z 1 (t), z 2 (t), t ≥ 0 defined by (6). We define,…”

“…Suppose also that u ∈ L 1 (0, +∞). Then the function u(t), t ≥ 0, is identifiable from the measurements z 1 (t), z 2 (t), t ≥ 0 obtained from (6).…”

“…Various techniques were used in the literature to investigate existence and uniqueness properties of weak and strong solutions [2], [3], [6], [1]. In [17], the observability problem for system (1), (2) was studied, and in [16] these results were employed to prove the distributed controllability.…”