It is well known that rate-independent systems involving nonconvex energy
functionals in general do not allow for time-continuous solutions even if the
given data are smooth. In the last years, several solution concepts were
proposed that include discontinuities in the notion of solution, among them
the class of global energetic solutions and the class of BV-solutions.
In general, these solution concepts are not equivalent and numerical schemes
are needed that reliably approximate that type of solutions one is interested
in. In this paper we analyze the convergence of solutions of three
schemes, namely an approach based on local minimization, a relaxed version
of it and an alternate minimization scheme. For all three cases we show that under
suitable conditions on the discretization parameters discrete solutions
converge to limit functions that belong to the class of BV-solutions. The
proofs rely on a reparametrization argument. We illustrate the different
schemes with a toy example.