Systems

A novel structure preserving scheme for Schrondiger-Poisson systems.

Dr. Th. Katsaounis

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B2 L5 R5220

In this talk I will present a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrodinger-Poisson system. We use the Crank-Nicolson scheme as a time-stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system’s mass conservation and energy balance laws for constant discretization parameters.

On some nonlinear elliptic/parabolic systems arising in mechanics and turbulence

Prof. Luigi Carlo Berselli

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B2 L5 R5220

I consider the vector counterpart of the classical p-Laplace and p-heat equations which are some of the building blocks for the mathematical description of non-linear plasticity, non-Newtonian fluids, and turbulent eddy viscosity models. I will discuss results of “natural regularity” and their role in the study of the well-posedness of the nonlinear pdes as well as in the theory of convergence for space-time discretisation methods. In particular, I will present the “A-approximation" method which generalises results by Necas and which reduces the problem to a family of linear ones. Coffee Time: 15:30 - 16:00