A Cut Discontinuous Galerkin Method for Coupled Bulk-Surface Problems
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured, unfitted background mesh. By adding certain stabilization terms to the discrete variational formulation of the coupled bulk-surface problem, the resulting cutDGM is provably stable and exhibits optimal convergence properties as demonstrated by numerical experiments. We also show both theoretically and numerically that the system matrix is well-conditioned, irrespective of the relative position of the bulk domain in the background mesh.
This work was supported in part by the Kempe foundation (JCK-1612). The author expresses his gratitude to Ceren Gürkan for her help with the set-up of the convergence experiment, to Erik Burman for his great editorial assistance during the preparation of this contribution, and finally, to the two anonymous referees for their valuable comments and suggestions.
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