A posteriori error estimates for discontinuous Galerkin method to the elasticity problem
This work provides theoretical error estimates for DG methods in time-dependent elasticity, which is valuable for numerical analysts and practitioners in computational mechanics, though the approach is an extension of existing reconstruction techniques.
The authors derive a posteriori error bounds for the discontinuous Galerkin method applied to time-dependent linear elasticity, using a stationary elasticity reconstruction technique. They present two error bounds for the stationary problem via L2 duality and energy norm, and extend the approach to fully discrete schemes with backward-Euler time stepping.
This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary elasticity reconstruction technique which allows to estimate the error for time-dependent problem through the error estimation of the associated stationary elasticity problem. To this end, to derive the error bound for the stationary problem, we present two methods to obtain two different a posteriori error bounds, by $L^2$ duality technique and via energy norm. For fully discrete scheme, we make use of the backward-Euler scheme and an appropriate space-time reconstruction. The technique here can be applicable for a variety of DG methods as well.