Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian

We generalize the a posteriori techniques for the linear heat equation in Verfürth (Calcolo 40(3):195–212, 2003) to the case of the nonlinear parabolic $p$ -Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of the error and the residual, which is the key property for proving the error bounds.