  When a numerical simulation has to handle a physics problem with a wide range
of time-dependent length scales, dynamically adaptive discretizations can be
the method of choice. We present a major upgrade to the numerical relativity
code bamps in the form of fully adaptive, physics-agnostic hp-refinement. We
describe the foundations of mesh refinement in the context of spectral element
methods, the precise algorithm used to perform refinement in bamps, as well as
several indicator functions used to drive it. Finally, we test the performance,
scaling, and the accuracy of the code in treating several 1d and 2d example
problems, showing clear improvements over static mesh configurations. In
particular, we consider a simple non-linear wave equation, the evolution of a
real scalar field minimally coupled to gravity, as well as nonlinear
gravitational waves.
