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We develop a stabilized cut finite element method for the stationaryconvection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cutfinite element method is based on using an embedding of the surface into athree dimensional mesh consisting of tetrahedra and then using the restrictionof the standard piecewise linear continuous elements to a piecewise linearapproximation of the surface. The stabilization consists of a standardstreamline diffusion stabilization term on the discrete surface and a so callednormal gradient stabilization term on the full tetrahedral elements in theactive mesh. We prove optimal order a priori error estimates in the standardnorm associated with the streamline diffusion method and bounds for thecondition number of the resulting stiffness matrix. The condition number is ofoptimal order $O(h^{-1})$ for a specific choice of method parameters. Numericalexample supporting our theoretical results are also included.

A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces