  The size of micromagnetic structures, such as domain walls or vortices, is
comparable to the exchange length of the ferromagnet. Both, the exchange length
of the stray field $l_s$ and the magnetocrystalline exchange length $l_k$ are
material-dependent quantities that usually lie in the nanometer range. This
emphasizes the theoretical challenges associated with the mesoscopic nature of
micromagnetism: the magnetic structures are much larger than the atomic lattice
constant, but at the same time much smaller than the sample size. In computer
simulations, the smallest exchange length serves as an estimate for the largest
cell size admissible to prevent appreciable discretization errors. This general
rule is not valid in special situations where the magnetization becomes
particularly inhomogeneous. When such strongly inhomogeneous structures
develop, micromagnetic simulations inevitably contain systematic and numerical
errors. It is suggested to combine micromagnetic theory with a Heisenberg model
to resolve such problems. We analyze cases where strongly inhomogeneous
structures pose limits to standard micromagnetic simulations, arising from
fundamental aspects as well as from numerical drawbacks.
