Grid adjustment for parabolic systems based on a posteriori error estimates

The construction of a one-dimensional space grid for solving a system of parabolic partial differential equations by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. Two a posteriori error estimators for the approximate solution are presented together with statements on their rate of convergence. Results obtained for a numerical example are shown in conclusion.