Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 293, Issue -, Pages 431-461Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2015.05.010
Keywords
Cut finite element method; Surfactants; PDEs on surfaces; Characteristic Galerkin method
Funding
- Swedish Foundation [AM13-0029]
- Swedish Research Council [2011-4992, 2013-4708, 2014-4804]
- Swedish strategic research programme eSSENCE
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We develop a finite element method for convection-diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant. The method is based on a characteristic-Galerkin formulation combined with a piecewise linear cut finite element method in space. The cut finite element method is constructed by embedding the surface in a background grid and then using the restriction to the surface of a finite element space defined on the background grid. The surface is allowed to cut through the background grid in an arbitrary fashion. To ensure stability and well posedness of the resulting algebraic systems of equations, independent of the position of the surface in the background grid, we add a consistent stabilization term. We prove error estimates and present confirming numerical results. (C) 2015 Elsevier B.V. All rights reserved.
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