Check libMesh restart capabilities.
Based on adaptivity_ex5.
libMesh should be configured with mpi, petsc and exodusII support.
Using spack:
spack install libmesh@master +mpi +petsc +exodusii
libMesh is found via pkgconfig, so make sure to have its folder available:
export PKG_CONFIG_PATH=$LIBMESH_DIR/lib[64]/pkgconfig