  We investigate the nonlinear evolution of the $m = 1$ resistive internal kink
mode in a two-dimensional (2D) configuration containing a central region of
negative current density, also known as the "current hole" setup. The
finite-element code FINMHD is used to solve a reduced set of incompressible
Magnetohydrodynamic (MHD) equations with a current-vorticity formulation.
First, the kink instability linearly develops in agreement with the general
theory of resistive internal kink mode, and it subsequently leads to the
formation of a current sheet. At relatively low Lundquist number $S$, a
magnetic reconnection process proceeds with a rate predicted by the
Sweet-Parker regime. Conversely, when $S$ exceeds a critical value that is $S_c
\simeq 10^4$, the current sheet is disrupted by the formation of plasmoids on a
slightly sub-Alfv\'enic time scale. In the latter case, a stochastic
reconnection regime exhibiting Petshek-type features enriched by plasmoids is
reached. A relatively fast normalized reconnection rate value of order $0.02$
is also measured. Finally, we compare our results with those obtained in
similar 2D previous studies using ideal MHD instabilities to initiate the
process, and discuss their relevance for the general theory of plasmoid chains
formation and associated fast reconnection regime.
