Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project B3Numerical Analysis of equivariant evolution equations09-048 Wolf-Jürgen Beyn, Janosch Rieger. We propose a set-valued version of the implicit Euler scheme for relaxed one-sided Lipschitz differential inclusions and prove that the defining implicit inclusions have a well-defined solution. Furthermore, we give a convergence analysis based on stability theorems, which shows that the set-valued implicit Euler method inherits all favourable stability properties from the single-valued scheme. The impact of spatial discretization is discussed, a fully discretized version of the scheme is analyzed, and a numerical example is given.
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