A posteriori error estimation for parabolic problems with dynamic boundary conditions

TL;DR

This paper develops reliable a posteriori error estimators for adaptive mesh refinement in parabolic problems with dynamic boundary conditions, enhancing accuracy and efficiency in numerical solutions.

Contribution

It introduces a posteriori error estimators based on a PDE-DAE reformulation, with proven reliability and efficiency, for better adaptive discretization of such problems.

Findings

Estimators are reliable and efficient.

Numerical experiments demonstrate improved local refinement.

Method enhances boundary treatment in adaptive schemes.

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.