Strict Discretization Error Bounds on Quantities of Interest in Transient Dynamics

Abstract

This work proposes a guaranteed error estimator for linear transient elastodynamics, accounting for both time and space discretization errors. The key lies in the definition of a novel dynamic constitutive relation error formulation, which is proven to be a strict bound of the discretization error. Moreover, based on the established dynamic constitutive relation error and the goal-oriented error estimation framework, strict upper and lower bounds on quantities of interest are also obtained. Numerical examples are conducted to verify the proposed strict bounds and to explore the application of these bounds to adaptive time stepping and mesh refinement.