Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

CEM - visualization and discovery in Email

This paper presents a lattice-based visual metaphor for knowledge discovery in electronic mail. It allows a user to navigate email using a visual lattice metaphor rather than a tree structure. By using such a conceptual multi-hierarchy, the content and shape of the lattice can be varied to accommodate any number of queries against the email collection. The system provides more flexibility in retrieving stored emails and can be generalised to any electronic documents. The paper presents the underlying mathematical structures, and a number of examples of the lattice and multi-hierarchy working with a prototypical email collection.