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A Multiscale Method for Heterogeneous Bulk-Surface Coupling

Altmann, Robert; Verfürth, Barbara ORCID iD icon


In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization of bulk and surface dynamics. This allows us to combine multiscale methods on the boundary with standard Lagrangian schemes in the interior. We prove convergence and quantify explicit rates for low-regularity solutions, independent of the oscillatory behavior of the heterogeneities. As a result, coarse discretization parameters, which do not resolve the fine scales, can be considered. The theoretical findings are justified by a number of numerical experiments including dynamic boundary conditions with random diffusion coefficients.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2021
Sprache Englisch
Identifikator KITopen-ID: 1000135768
Nachgewiesen in arXiv
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