THE ‘NO BOUNDARY CONDITION’ OUTFLOW BOUNDARY CONDITION

We use a one-dimensional model problem of advection– diffusion to investigate the treatment recently advocated by Papanastasiou and colleagues to deal with boundary conditions at artificial outflow boundaries. Using finite elements of degree p, we show that their treatment is equivalent to imposing the condition that the (p+1 )st derivative of the dependent variable should vanish at a point close to the outflow. This is then shown to lead to errors of order 𝒪((h+1/Pe)1.6^p+1) in the numerical solutions (where h is the maximum element size and Pe is the global Peclet number), which is superior to the errors of order 𝒪(h^p+1+1/Pe) obtained using a standard no-flux outflow condition. These findings are verified by numerical experiments. © 1997 by John Wiley and Sons, Ltd.