  The problem of solving partial differential equations (PDEs) on manifolds can
be considered to be one of the most general problem formulations encountered in
computational multi-physics. The required covariant forms of balance laws as
well as the corresponding covariant forms of the constitutive closing relations
are naturally expressed using the bundle-valued exterior calculus of
differential forms or related algebraic concepts. It can be argued that the
appropriate solution method to such PDE problems is given by the finite element
exterior calculus (FEEC). The aim of this essay is the exposition of a simple,
efficiently-implementable framework for general hp-adaptivity applicable to the
FEEC on higher-dimensional manifolds. A problem-independent spectral
error-indicator is developed which estimates the error and the spectral decay
of polynomial coefficients. The spectral decay rate is taken as an
admissibility indicator on the polynomial order distribution. Finally, by
elementary computational examples, it is attempted to demonstrate the power of
the method as an engineering tool.
