Abstract
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 τ is sufficiently small, the proposed algorithm yields for finite time T an error of O ( h 2 + τ ) in the L 2 -norm for the displacement field u and an error estimate of O ( h + τ ) in the H 1 -norm, where h is the mesh size. In addition, under stronger initial conditions we obtain an error estimate of O ( h + τ ) in the L 2 -norm for the divergence field ϕ .
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