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), 221-24. pdf
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.
15.
A. Demlow, J. Guzmán and A. Schatz,
Local energy estimates for the
finite element method on sharply varying grids. Math. Comp. 80 (2011), no.
273, 1-9.
16.
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.
17.
B. Cockburn, J. Gopalakrishnan and J. Guzmán, A new elasticity element made for
enforcing weak stress symmetry, Math. Comp., 79 (2010), 1331-1349.
18.
J. Gopalakrishnan and J. Guzmán, A second elasticity element using the matrix
bubble, IMA J. Numer. Anal., to appear.
19.
J.
Guzmán, A unified analysis of several
mixed methods for elasticity with weak stress symmetry, J. Sci. Comp., 44
(2010), 156-169.
20.
E.M.
Behrens and J. Guzmán, A mixed method for
the biharmonic problem based on a system of first-order equations, SIAM J.
Numer. Anal., 49 (2011), 789-817.
21.
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. Model, 8(2011), no. 1, 28-47.
22.
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, J.
Sci. Comp, 49 (2011), 137-16.
23. J. Guzmán and D. Leykekhman, Pointwise error estimates of finite element
approximations to the Stokes problem on convex polyhedra, Math. Comp., 81
(2012), 1879-2002.
24.
J. Gopalakrishnan and J. Guzmán, Symmetric non-conforming mixed finite
elements for linear elasticity, SIAM J. Numer. Anal., 49 (2011), 1504-1520.
25.
B. Cockburn, J. Guzmán, F.J.
Sayas, Coupling of RT and HDG with BEM, SIAM J. Numer. Anal., 50 (2012), no. 5, 2778–2801.
26.
J.
Guzmán and M. Neilan, A family of non-conforming
elements for the Brinkman problem, IMA J. Num. Anal., 32 (2012), no. 4, 1484–1508.
27.
J. Guzmán, D. Leykekhman and M. Neilan, A family
of non-conforming elements and analysis of Nitsche’s method for a singularly
perturbed fourth-order problem, Calcolo, 49 (2012), 95-125.
28.
J.
Guzmán and M. Neilan, Conforming and
divergence free Stokes elements on general triangular meshes, Math. Comp., 83 (2014), no. 285, 15–36.
29.
J.
Guzmán, A. Salgado and F.-J. Sayas, A
note one the Ladyzenskaja-Babuska-Brezzi Condition, J. Sci. Comp., 56 (2013), no. 2, 219–229.
30.
J. Guzmán and M. Neilan, Conforming and symmetric mixed finite
elements for plane elasticity using rational bubbles, Numer. Math., to appear.
31.
T. Gudi and J. Guzmán, Convergence analysis of the lowest order weakly penalized adaptive
discontinuous Galerkin methods, M2AN, to appear.
32. S. Badia, R. Codina, T. Gudi and J. Guzmán, Error Analysis of Discontinuous Galerkin Methods for Stokes Problem under Minimal Regularity, IMA J. Numer. Anal., to appear. pdf
33. D. Arnold, R. Falk, J. Guzmán and G. Tsogtgerel, On the consistency of the combinatorial codifferential, Trans. Amer. Math. Soc., to appear. pdf
34.
J. Guzmán and M. Neilan, Conforming and divergence free Stokes
elements in three dimensions, IMA J. Numer. Anal, to appear.
35. J. Guzman and M. Sanchez, Max-norm stability of lowest order Taylor-Hood elements in three dimensions, submitted. pdf
36. J. Guzman and C. Klivans, Chip firing and energy minimization on M-matrices, submitted. pdf