Abstract

One of the simplest model problems in the kinetic theory of plasma--physics is the Vlasov-Poisson system with periodic boundary conditions. Such system describes the evolution of a plasma of charged particles (electrons and ions) under the effects of the transport and self-consistent electric field. In this talk, we present a family of discontinuous Galerkin (DG) methods for the approximation of the Vlasov-Poisson system.

We shall discuss the error and convergence analysis and the properties of the proposed methods. We also present numerical experiments in the 1D case that validate the theory. 

If time allows, in the last part of the talk, we shall discuss the possibility of combining the proposed methods with some dimension reduction techniques, such as sparse grids. 

The talk is based on joint works  with Saverio Castelanelli (UAB-CRM), J.A. Carrillo (Imperial College, UK), Soheil Hajian (Univ. Geneva) and Chi-Wang Shu (Brown University, US)

Biography

Blanca Ayuso de Dios received her Phd in Mathematical Sciences from Universidad Autonoma de Madrid (Spain) in October 2003. She then took a postdoctoral position at the Istituto di Matematica Applicata e Tecnologie Informatiche ( IMATI-CNR) at  Pavia (Italy) where she was working  for more than three years. She came back to Madrid on January 2007 as an Assistant Professor and since January 2010, she works at the Centre de Recerca Matematica at Barcelona, with  a Ramon y Cajal contract  (Government Tenure-Track Research position).

Her research is mainly concerned with the development and analysis of numerical methods (mainly of finite element type) for Partial Differential Equations. 

She has been also very active in the analysis and development of fast solvers for the algebraic systems arising from the numerical discretizations; in particular  domain decomposition and multilevel methods.

The applications in which she works, are mostly related to Continuum-Mechanics and Plasma Physics.