@article{1795453, abstract = {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.}, author = {Beyn, Wolf-Jürgen and Rieger, Janosch}, issn = {1531-3492}, journal = {Discrete And Continuous Dynamical Systems. Series B}, number = {2}, pages = {409--428}, publisher = {American Institute of Mathematical Sciences}, title = {{The implicit Euler scheme for one-sided Lipschitz differential inclusions}}, doi = {10.3934/dcdsb.2010.14.409}, volume = {14}, year = {2010}, }