Summary.For the Laplace equation with Signorini boundary conditions two equivalent boundary variational inequality formulations are deduced. We investigate the discretization by a boundary element Galerkin method and obtain quasi-optimal asymptotic error estimates in the underlying Sobolev spaces. An algorithm based on the decomposition-coordination method is used to solve the discretized problems. Numerical examples confirm the predicted rate of convergence.

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A method is described using the polymerase chain reaction (PCR) to amplify defined nucleic acid strands in individual cells in situ in conventional smears of bone marrow and peripheral cells. Using radioactively labeled precursors, the incorporation into newly synthesized strands by PCR can be detected by microautoradiography. The specificity of the method can be monitored by gel electrophoresis of the material shed into the reaction mixture. Thus it could be shown that even single genes in individual cells can be amplified to visibility. In a mixture of HIV infected and non infected cells both can be clearly distinguished from one another.

An abstract error estimate for the approximation of semicoercive variational inequalities is obtained provided a certain condition holds for the exact solution. This condition turns out to be necessary as is demonstrated analytically and numerically. The results are applied to the finite element approximation of Poisson's equation with Signorini boundary conditions and to the obstacle problem for the beam with no fixed boundary conditions. For second order variational inequalities the condition is always satisfied, whereas for the beam problem the condition holds if the center of forces belongs to the interior of the convex hull of the contact set. Applying the error estimate yields optimal order of convergence in terms of the mesh size h. The numerical convergence rates observed are in good agreement with the predicted ones.

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