We present a linear backward Euler fully discrete finite volume method for the initial-boundary-value problem of purely longitudinal motion of a homogeneous bar and an give optimal order error estimates in and norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution in norm. Numerical experiment illustrates the convergence and stability of this scheme.
"The Backward Euler Fully Discrete Finite Volume Method for the Problem of Purely Longitudinal Motion of a Homogeneous Bar." Abstr. Appl. Anal. 2012 (SI10) 1 - 23, 2012. https://doi.org/10.1155/2012/475801