Publications

    

Journal Articles (accepted / submitted)

  1. J. Guzmán, Quadrature and Schatz's pointwise estimates in finite element methods, BIT 45 (2005), 695-707. preprint

  2. J. Guzmán, Local analysis of  discontinuous Galerkin methods applied to singularly perturbed problems, J. Numer. Math. 14 (2006), 41-56. preprint

  3. J. Guzmán, Pointwise estimates for discontinuous Galerkin methods with lifting operators for elliptic problems, Math. Comp. 75 (2006), 1067-1085. preprint

  4. B. Cockburn and J. Guzmán, Error estimates for the Runge-Kutta discontinuous Galerkin method for the transport equation with discontinuous initial data, SIAM J. Numer. Anal., accepted. preprint

  5. J. Guzmán, Local and pointwise error estimates of the local discontinuous Galerkin method for Stokes Problem, Math. Comp., accepted. preprint

  6. B. Cockburn, B. Dong and J. Guzmán, Optimal convergence of the original discontinuous Galerkin method for the transport-reaction equation on special meshes, SIAM J. Numer. Anal., accepted. preprint

  7. B. Cockburn, B. Dong and J. Guzmán, A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems, Math Comp., accepted.

  8. E. Burman, J. Guzmán and D. Leykekhman, Weighted error estimates of the continuous interior penalty method for singularly perturbed problems, IMA J. Numer. Anal., accepted.

  9. B. Cockburn, J. Guzmán and H. Wang, Superconvergent discontinuous Galerkin methods for second-order elliptic problems, submitted.

  10. J. Guzmán, D. Leykekhman, J. Rossmann and A. Schatz, Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods, submitted.

Articles in Preparation

  1. B. Cockburn, B. Dong and J. Guzmán, A superconvergent LDG-hybridizable Galerkin method for the biharmonic problem, in preparation.

  2. B. Cockburn, B. Dong, J. Guzmán, M. Restelli and R. Sacco, Superconvergent discontinuous Galerkin methods for general second-order elliptic problems, in preparation.

  3. B. Cockburn, J. Guzmán, C.-S. Soon and H. Stolarski, Analysis of the embedded discontinuous Galerkin method, in preparation.