A posteriori error estimation for parabolic problems with dynamic boundary conditions

2023/02/06 by Robert Altmann, Altmann, Robert, Christoph Zimmer +1
Engineering · Mathematics · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2302.02893

Abstract

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.

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