  In this work, we analyze the residual-based a posteriori error estimation of
the multi-scale cancer invasion model, which is a system of three
non-stationary reaction-diffusion equations. We present the numerical results
of a study on a posteriori error control strategies for FEM approximations of
the model. In this paper, we derive a residual type error estimator for the
cancer invasion model and illustrate its practical performance on a series of
computational tests in three-dimensional spaces. We show that the error
estimator is reliable and efficient regarding the model's small perturbation
parameters.
