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.

翻译：本文关注具有动态边界条件的抛物型问题空间离散的自适应网格细化策略。作为前期步骤，本研究首先针对稳态模型问题刻画了满足inf-sup稳定的离散格式。基于将该系统重新表述为偏微分代数方程，我们引入了后验误差估计子，该估计子既能实现局部细化，又能对边界进行特殊处理。我们证明了估计子的可靠性与有效性，并通过多个数值实验展示了其性能。