Numerical Analysis of equivariant evolution equations
09-048 Wolf-Jürgen Beyn, Janosch Rieger.
The implicit Euler scheme for one-sided Lipschitz differential inclusions
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.
