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A cut finite element method for coupled bulk-surface problems on time-dependent domains
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 307, 96-116 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh.

Place, publisher, year, edition, pages
2016. Vol. 307, 96-116 p.
Keyword [en]
Coupled bulk-surface problems, Cut finite element method (CutFEM), Space-time FEM, Evolving mains, Soluble surfactant, Sharp interface method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-124135DOI: 10.1016/j.cma.2016.04.012ISI: 000378055900005OAI: oai:DiVA.org:umu-124135DiVA: diva2:951109
Available from: 2016-08-05 Created: 2016-07-21 Last updated: 2016-08-05Bibliographically approved

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Larson, Mats G.
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Department of Mathematics and Mathematical Statistics
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