3 research outputs found
A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces
We develop a stabilized cut finite element method for the stationary convection diffusion problem
on a surface embedded in R
d
. The cut finite element method is based on using an embedding of the
surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the
standard piecewise linear continuous elements to a piecewise linear approximation of the surface.
The stabilization consists of a standard streamline diffusion stabilization term on the discrete
surface and a so called normal gradient stabilization term on the full tetrahedral elements in the
active mesh. We prove optimal order a priori error estimates in the standard norm associated with
the streamline diffusion method and bounds for the condition number of the resulting stiffness
matrix. The condition number is of optimal order for a specific choice of method parameters.
Numerical examples supporting our theoretical results are also included