Adaptive strategy for transient/coupled problems applications to thermoelasticity and elastodynamics

Error Assessment in Structural Transient Dynamics

“…An analogous rationale holds for assessing the total energy of the error, ||e v (T )|| 2 m + ||e u (T )|| 2 a , see references [34,53]. Here, the L 2 -norm of the error is seen as a particular quantity of interest to be estimated using the DWR approach presented in section 5.1.…”

“…In this context, different estimates provide also indicators driving mesh adaptive procedures, either using energy-like measures [29,30,31,32,33,34] or QoI [35,36,37,38]. Estimates providing error bounds are also available both for energy-like error measures [39,40,41] and goal-oriented ones [42,43,44,45,46,47,31].…”

Computable bounds of functional outputs in linear visco-elastodynamics

“…The error estimation tools dealing with transient problems are not so popular, especially in the case of structural dynamics. Some of the contributions on this last topic are, on the one hand, the energy error estimates presented by Aubry et al [8], Li and Wiberg [9,10] and Ladevèze et al [11,12,13,14] and, on the other hand, the goal-oriented estimates proposed by Schleupen and Ramm [15], Fuentes et al [16] and Ladevèze and co-workers [17,18,19,20].…”

Space‐time finite elements and an adaptive strategy for the coupled thermoelasticity problem

“…However, as it appears from the literature, very little attention has been paid to error estimation and adaptive ÿnite element techniques, e.g. Aubry et al [1]. In this paper, we propose a new ÿnite element formulation with space-time ÿnite elements that is based on the standard Galerkin method in space (piecewise linear approximations for both the displacement and temperature ÿelds) and the discontinuous Galerkin method in time (piecewise constant approximation).…”