@TechReport{ it:2013-004,
author = {Peter Hansbo and Mats G. Larson and Sara Zahedi},
title = {Characteristic Cut Finite Element Methods for
Convection-Diffusion Problems on Time Dependent Surfaces},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2013},
number = {2013-004},
month = mar,
abstract = {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 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.}
}