MiS Preprint Repository

The numerical treatment of the hyperbolic system of nonlinear wave equations with linear viscosity, $u_{ii}=div(\sigma (Du)+D{u}_i)$, is studied for a large class of globally Lipschitz continuous functions $\sigma$, including non-monotone stress-strain relations. The analyzed method combines an implicit Euler scheme in time with Courant (continuous and piecewise affine) finite elements in space for general time steps with varying meshes. Explicit a priori error bounds in $L^{\mathrm{\infty }}(L^2)$, $L^2(W^{1,2})$, and $W^{1,2}(L^2)$ are established for the solutions of the fully discrete scheme.