This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a stationary model problem as a preliminary step. Based on an alternative formulation of the system as a partial differential-algebraic equation, we introduce a posteriori error estimators which allow local refinements as well as a special treatment of the boundary. We prove reliability and efficiency of the estimators and illustrate their performance in several numerical experiments.
@article{arxiv.2302.02893,
title = {A posteriori error estimation for parabolic problems with dynamic boundary conditions},
author = {Robert Altmann and Christoph Zimmer},
journal= {arXiv preprint arXiv:2302.02893},
year = {2023}
}