  Adaptive finite element methods are a powerful tool to obtain numerical
simulation results in a reasonable time. Due to complex chemical and mechanical
couplings in lithium-ion batteries, numerical simulations are very helpful to
investigate promising new battery active materials such as amorphous silicon
featuring a higher energy density than graphite. Based on a thermodynamically
consistent continuum model with large deformation and chemo-mechanically
coupled approach, we compare three different spatial adaptive refinement
strategies: Kelly-, gradient recovery- and residual based error estimation. For
the residual based case, the strong formulation of the residual is explicitly
derived. With amorphous silicon as example material, we investigate two 3D
representative host particle geometries, reduced with symmetry assumptions to a
1D unit interval and a 2D elliptical domain. Our numerical studies show that
the Kelly estimator overestimates the error, whereas the gradient recovery
estimator leads to lower refinement levels and a good capture of the change of
the lithium flux. The residual based error estimator reveals a strong
dependency on the cell error part which can be improved by a more suitable
choice of constants to be more efficient. In a 2D domain, the concentration has
a larger influence on the mesh distribution than the Cauchy stress.
