Past Forthcoming Seminars

23 February 2004
Stanislav Volkov
We consider a queuing system with three queues (nodes) and one server. The arrival and service rates at each node are such that the system overall is overloaded, while no individual node is. The service discipline is the following: once the server is at node j, it stays there until it serves all customers in the queue. After this, the server moves to the "more expensive" of the two queues. We will show that a.s. there will be a periodicity in the order of services, as suggested by the behavior of the corresponding dynamical systems; we also study the cases (of measure 0) when the dynamical system is chaotic, and prove that then the stochastic one cannot be periodic either.
  • Stochastic Analysis Seminar
20 February 2004
Dr Peter Bastian
Discontinuous Galerkin methods (DG) use trial and test functions that are continuous within elements and discontinuous at element boundaries. Although DG methods have been invented in the early 1970s they have become very popular only recently. \\ DG methods are very attractive for flow and transport problems in porous media since they can be used to solve hyperbolic as well as elliptic/parabolic problems, (potentially) offer high-order convergence combined with local mass balance and can be applied to unstructured, non-matching grids. \\ In this talk we present a discontinuous Galerkin method based on the non-symmetric interior penalty formulation introduced by Wheeler and Rivi\`{e}re for an elliptic equation coupled to a nonlinear parabolic/hyperbolic equation. The equations cover models for groundwater flow and solute transport as well as two-phase flow in porous media. \\ We show that the method is comparable in efficiency with the mixed finite element method for elliptic problems with discontinuous coefficients. In the case of two-phase flow the method can outperform standard finite volume schemes by a factor of ten for a five-spot problem and also for problems with dominating capillary pressure.
  • Computational Mathematics and Applications Seminar