WIAS Preprint No. 2196, (2015)

A posteriori error control for stationary coupled bulk-surface equations


Authors

  • Eigel, Martin
    ORCID: 0000-0003-2687-4497
  • Müller, Rüdiger
    ORCID: 0000-0003-2643-722X

2010 Mathematics Subject Classification

  • 65N30 65N15 58J32 65M15 74S05 65M60

Keywords

  • finite element method, a posteriori error estimator, adaptive algorithm, surface finite elements, bulk-surface elliptic equations

DOI

10.20347/WIAS.PREPRINT.2196

Abstract

We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm with several benchmark examples.

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