Publications

 

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

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

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

4.     J. Guzmán, Local and pointwise error estimates of the local discontinuous Galerkin method for Stokes Problem, Math. Comp 77 (2008), 1293-1322.  

5.     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 48 (2008), 1250-1265.  

6.     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.  46 (2008), 1364-­1398.  

7.     B. Cockburn, B. Dong and J. Guzmán, A superconvergent LDG-­hybridizable Galerkin method for second­order elliptic problems, Math. Comp. 77 (2008), 1887-1916.

8.     B. Cockburn, J. Guzmán and H. Wang, Superconvergent discontinuous Galerkin methods for second­order elliptic problems, Math. Comp., 78 (2009), 1-24.

9.     E. Burman, J. Guzmán and D. Leykekhman, Weighted error estimates of the continuous interior penalty method for singularly perturbed problems, IMA J. Numer. Anal., 29 (2009), 284-314. 

10.   J. Guzmán, and B. Riviere, Sub­optimal convergence of non­symmetric discontinuous Galerkin method for odd polynomial approximations, J. Sci. Comput., 40 (2009), 273-280.

11.   J. Guzmán, D. Leykekhman, J. Rossmann and A. Schatz, Hölder estimates for Greens functions on convex polyhedral domains and their applications to finite element methods, Numer. Math., 112 (2009), 221-243.

12.  B. Cockburn, B. Dong and J. Guzmán, A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems, J. Sci. Comp., 40 (2009), 141-187.

13.  B. Cockburn, J. Guzmán, C.­-S. Soon and H. Stolarski, Analysis of the embedded discontinuous Galerkin method for second­-order elliptic problems, SIAM J. Numer Anal., 47(2009), no. 4, 2686-2707.  

14.  B. Cockburn, B. Dong, J. Guzmán, M. Restelli and R. Sacco, A hybridizable discontinuous Galerkin method for steady state convection-­diffusion-­reaction problems, SIAM J. Sci. Comp., 31 (2009), no. 5, 3827-3846.

1.     A. Demlow, J. Guzmán, and A.H. Schatz, Local energy estimates for the finite element method on sharply varying grids, Math Comp., to appear.

2.     B. Cockburn, B. Dong, J. Guzmán and J. Qian, Optimal convergence of the original DG method in special meshes for variable velocity, SIAM J. Numer. Anal., 48 (2010), no. 1, 133-146.

3.     B. Cockburn, J. Gopalakrishnan and J. Guzmán, A new elasticity element made for enforcing weak stress symmetry, Math. Comp.,  79 (2010), 1331-1349.

4.     J. Gopalakrishnan and J. Guzmán, A second elasticity element using the matrix bubble with tightened stress symmetry, submitted.

5.     J. Guzmán, A unified analysis of several mixed methods for elasticity with weak stress symmetry, J. Sci. Comp., 44 (2010), 156-169.

6.      E.M. Behrens and J. Guzmán, A mixed method for the biharmonic problem based on a system of first-order equations, submitted.

7.     W. Wang, J. Guzmán, and C.-W. Shu, The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients, Int. J. Numer. Anal., to appear.

8.      E.M. Behrens and J. Guzmán, A new family of mixed methods for the Reissner-Mindlin plate model based on a system of first-order equations, submitted.

9.     J. Guzmán  and D. Leykekhman, Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra, submitted.     

10.   J. Gopalakrishnan and J. Guzmán, Symmetric non-conforming mixed finite elements for linear elasticity, submitted.