  The nonlinear magnetic induction equation with Hall effect can be used to
model magnetic fields, e.g. in astrophysical plasma environments. In order to
give reliable results, numerical simulations should be carried out using
effective and efficient schemes. Thus, high-order stable schemes are
investigated here.
  Following the approach provided recently by Nordstr\"om (J Sci Comput 71.1,
pp. 365--385, 2017), an energy analysis for both the linear and the nonlinear
induction equation including boundary conditions is performed at first. Novel
outflow boundary conditions for the Hall induction equation are proposed,
resulting in an energy estimate. Based on an energy analysis of the initial
boundary value problem at the continuous level, semidiscretisations using
summation by parts (SBP) operators and simultaneous approximation terms are
created. Mimicking estimates at the continuous level, several energy stable
schemes are obtained in this way and compared in numerical experiments.
Moreover, stabilisation techniques correcting errors in the numerical
divergence of the magnetic field via projection methods are studied from an
energetic point of view in the SBP framework. In particular, the treatment of
boundaries is investigated and a new approach with some improved properties is
proposed.
