The effect of mesh modification in time on the error control of fully discrete approximations for parabolic equations

We consider fully discrete schemes for linear parabolic problems discretized by the Crank–Nicolson method in time and the standard finite element method in space. We study the effect of mesh modification on the stability of fully discrete approximations as well as its influence on residual-based a posteriori error estimators. We focus mainly on the qualitative, analytical and computational behavior of the schemes and the error estimators.