**MSC:**- 35R30 Inverse problems (undetermined coefficients, etc.) for PDE
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

\[\Delta u -2h^{-1}(\nabla h, \nabla u=g) \]

We assume that the unknown function $u$ the straemfunction for a

class of flow problems is constant on certain parts of the boundary

$\partial\Omega$ while at the remaining parts no boundary condition

is imposed.

Instead, values of the gradient of $u$ (velocities) are prescribed at

a finite set $M$ of inner points (measuring points).

We look for the mimimizer of a functional being a combination of the

squared errors at the measuring points and for regularization a

squared $H^{1/2}$-norm of the (unknown) boundary values.

We present numerical solutions to the problem. Especially, the

dependence on the regularization parameter $\mu$ is discussed.