Behavior in the Large of Numerical Solutions to One-Dimensional Nonlinear Viscoelasticity by Continuous Time Galerkin Methods.

摘要

We analyze the long time behavior of fully discrete solutions to a one-dimensional nonlinear viscoelastic problem. It is shown that these approximations which are found by a continuous time Galerkin method converge to a steady state. The possible numerical steady states are characterized and in particular their high degree of dependence on initial data and mesh design is explained. Computational results are included which show the above dependence and indicate that the numerical solutions will typically not converge to unstable states. Keywords: Dynamic relation. (KR)