A priori error estimates for explicit finite element for linear elasto-dynamics by Galerkin method and central difference method

The explicit finite element method for transient dynamics of linear elasticity is formulated by using Galerkin method for space and the central difference method for time. An a priori error estimate is derived and the optimal rate of convergence for displacement similar to the linear elliptic problem is found. The error estimation is extended to velocity, internal (strain) energy and kinetic energy for engineering applications. The approximation error of initial data is analyzed. The error estimate is refined for a class of engineering applications with zero initial deformation and initial force. Examples of a 1-D rod axial vibration and a 2-D plate in-plane vibration are solved using linear elements as verification.