  In this paper, we introduce an invariant-region-preserving (IRP) limiter for
the p-system and the corresponding viscous p-system, both of which share the
same invariant region. Rigorous analysis is presented to show that for smooth
solutions the order of approximation accuracy is not destroyed by the IRP
limiter, provided the cell average stays away from the boundary of the
invariant region. Moreover, this limiter is explicit, and easy for computer
implementation. A generic algorithm incorporating the IRP limiter is presented
for high order finite volume type schemes as long as the evolved cell average
of the underlying scheme stays strictly within the invariant region. For any
high order discontinuous Galerkin (DG) scheme to the p-system, sufficient
conditions are obtained for cell averages to stay in the invariant region. For
the viscous p-system, we design both second and third order IRP DG schemes.
Numerical experiments are provided to test the proven properties of the IRP
limiter and the performance of IRP DG schemes.
