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

Authors:
Christian Kreuzer
Affiliations:
Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany 44801
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2013

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Abstract

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.