My research is mostly concerned with the development and analysis of numerical methods (mainly finite elements of different types) for Partial Differential Equations.

I am 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.  More recently I am interested in the approximation of high dimensional problems. The applications in which I work, are mostly related to Continuum-Mechanics and Plasma Physics.

• B. Ayuso de Dios, J.A. Carrillo and C.W. Shu, Discontinuous Galerkin Methods for the Multidimensional Vlasov-Poisson system, Mathematical Models and Methods in Applied Sciences (M3AS) M3AS, vol. 22, no. 12, (2012). [45 pages]
• B. Ayuso de Dios and Ludmil Zikatanov, Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations, Journal of Scientific Computing, vol. 40, no.1-3, pp. 4--36, (2009).
  
• B. Ayuso and L. Donatella Marini, Discontinuous Galerkin Approximation to advection-difusion-reaction problems, SIAM J. of Numer. Anal., vol. 47, no. 2, pp. 1391--1420, (2009).
• B. Ayuso de Dios, M.Holst, Y. Zhu and L.T. Zikatanov, Multilevel Preconditioners for Discontinuous Galerkin discretizations of jump-coefficient problems, Mathematics of Computation, 10.1090/S0025-5718-2013-02760-3, (Link)
• B. Ayuso, J.A. Carrillo and C.W. Shu, Discontinuous Galerkin Methods for the onedimensional Vlasov-Poisson system, Kinetic and Related Models, Vol 4, no 4, pp. 955--989 (2011).

[June 1996:]   Bachelor in Mathematical Science,  Universidad Autonoma de Madrid. Spain

[June 1999:]  Licenciada con Grado in Mathematical Sciences, Departamento de Matematicas de la Universidad Autonoma de Madrid. Spain

[October 2003:] PhD in Mathematical Science, Universidad Autonoma de Madrid. Spain

Thesis:  The postprocessed mixed finite element method for the Navier-Stokes equations