This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.
and T. C.Massey
, Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 3331–3346.
, Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems, Comput. Methods Appl. Mech. Engrg., 198 (2009), pp. 3113–3129.
, Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems, Math. Comp., 80 (2011), pp. 1335–1367.
, A numerical approach to space-time finite elements for the wave equation, J. Comput. Phys, 226 (2007), pp. 466–476.
, Superconvergence of the local discontinuous Galerkin method applied to the one-dimensional second-order wave equation, Numer. Part. Diff. Equ., 30 (2013), pp. 862–901.
, Discontinuous Galerkin methods for delay differential equations of pantograph type, SIAM J. Numer. Anal., 48 (2010), pp. 1944–1967.
, Superconvergence of discontinuous Galerkin method for linear hyperbolic equations, SIAM. J. Numer. Anal., 52-5 (2014), pp. 2555–2573.
, Superconvergence of local discontinuous Galerkin method for one-dimensional linear parabolic equations, Math. Comp, 85 (2016), pp. 63–84.
, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, J. Comput. Phys., 227 (2008), pp. 9612–9627.
, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension, SIAM J. Numer. Anal., 47 (2010), pp. 4044–4072.
, Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media, J. Comp. Phys., 272 (2014), pp. 88–107.
, Optimal discontinous Galerkin methods for wave propagation, SIAM J. Numer. Anal., 44 (2006), pp. 2131–2158.
, Optimal discontinous Galerkin methods for the acoustic wave equation in higher dimension, SIAM J. Numer. Anal., 47 (2009), pp. 3820–3848.
, Discontinuous Galerkin methods for ordinary differential equations, Math. Comp.
36 (1981), pp. 455–473.
, Symplectic finite difference approximations of the nonlinear klein-Gordon equation, SIAM. J. Numer. Anal, 34 (1997), pp. 1742–1760.
and T. E.Peterson
, A continuous space-time finite element method for the wave equation, Math. Comp., 65 (1996), pp. 491–506.
, Finite-difference schemes for nonlinear wave equation that inherit energy conservation property, J. Comp. Appl. Math., 134 (2001), pp. 37–57.
, Strong stability-preserving high-order time discretization methods, SIAM Rev., 43 (2001), pp. 89–112.
, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: eigen-structure analysis based on Fourier approach, J. Comput. Phys., 235 (2013), pp. 458–485.
, Superconvergence of a discontinuous Galerkin method for first-order linear delay differential equations, J. Comp. Math., 29 (2011), pp. 574–588.
, Uniform superconvergence analysis of the discontinuous Galerkin method for a singularly perturbed problem in 1-D, Math. Comp., 79 (2010), pp. 35–45.
Energy conserving discontinous Galerkin methods for wave propagation problems, Inverse Problems and Imaging, 7 (2013), pp. 967–986.
, Analysis of optimal supercovergence of discontinuous Galerkin method for linear hyperbolic equations, SIAM J. Numer. Anal., 50 (2012), pp. 3110–3133.
, Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations, J. Comp.Math., 33 (2015), pp. 323–340.
, Superconvergence of discontinuous Galerkin methods for convection-diffusion problems, J. Sci. Comput., 41 (2009), pp. 70–93.