Kurt Frischmuth, Michael Hänler
On the inverse problem for the Ekman equation
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract: We consider inverse problems for the partial differential equation
\[\Delta u -2h^{-1}(\nabla h, \nabla u=g) \]
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.
Keywords: Elliptic boundary value problems, inverse problems