The finite element analysis of a fractional-step method for the time-dependent linear elasticity equations

This paper provides a convergence analysis of a fractional-step method for time-dependent system of equations of linear elasticity by means of finite element approximations. Error estimates in finite time are given. And it is verified that provided the time-step ττ is sufficiently small, the proposed algorithm yields for finite time TT an error of O(h2+τ)O(h2+τ) in the L2L2-norm for the displacement field u and an error estimate of O(h+τ)O(h+τ) in the H1H1-norm, where hh is the mesh size. In addition, under stronger initial conditions we obtain an error estimate of O(h+τ)O(h+τ) in the L2L2-norm for the divergence field ϕϕ.