The backward Euler fully discrete finite volume method for the problem of purely longitudinal motion of a homogeneous bar
Summary: 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 give an optimal order error estimates in \(L^2\) and \(H^1\) norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution \(u\) in \(H^1\) norm. Numerical experiment illustrates the convergence and stability of this scheme.
scientific article; zbMATH DE number 6134098