Solution of the three-dimensional convection-diffusion equation by means of the Finite Element Method - Biomechanics: Concepts and Computation - page 294

c ∇ 16.5 If the flux n · u = P along p is prescribed, the integral (element level):

∼ Pd ,

e

needs to be computed. It may be transformed to the local coordinate system
ξ ∈ −

[ 1 1], such that:

1

∼ P ∂

x
∂ξ

∼ Pd = d ξ ,

e − 1

where it is assumed that e is oriented in x-direction.
If linear elements are chosen, the shape functions along the boundary are
given by:

2 (1 .

− ξ )

∼ =

1

2 (1 + ξ )

Use an isoparametric element and let L denote the length of e , then

demonstrate that for constant P :

1
1

.

LP
2

∼ Pd =

e