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.

Mining minimal non-redundant association rules using frequent closed itemsets

The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, real-life databases lead to several thousands association rules with high confidence and among which are many redundancies. Using the closure of the Galois connection, we define two new bases for association rules which union is a generating set for all valid association rules with support and confidence. These bases are characterized using frequent closed itemsets and their generators; they consist of the non-redundant exact and approximate association rules having minimal antecedents and maximal consequences, i.e. the most relevant association rules. Algorithms for extracting these bases are presented and results of experiments carried out on real-life databases show that the proposed bases are useful, and that their generation is not time consuming.