  With the increasing number of components and further miniaturization the mean
time between faults in supercomputers will decrease. System level fault
tolerance techniques are expensive and cost energy, since they are often based
on redundancy. Also classical check-point-restart techniques reach their limits
when the time for storing the system state to backup memory becomes excessive.
Therefore, algorithm-based fault tolerance mechanisms can become an attractive
alternative. This article investigates the solution process for elliptic
partial differential equations that are discretized by finite elements. Faults
that occur in the parallel geometric multigrid solver are studied in various
model scenarios. In a standard domain partitioning approach, the impact of a
failure of a core or a node will affect one or several subdomains. Different
strategies are developed to compensate the effect of such a failure
algorithmically. The recovery is achieved by solving a local subproblem with
Dirichlet boundary conditions using local multigrid cycling algorithms.
Additionally, we propose a superman strategy where extra compute power is
employed to minimize the time of the recovery process.
