Asymptotically Exact Posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Nonlinear Convection–Diffusion Problems

[1]  Yao Cheng,et al.  Application of generalized Gauss-Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations , 2016, Math. Comput..

[2]  Mahboub Baccouch.  Optimal a posteriori error estimates of the local discontinuous Galerkin method for convection-diffusion problems in one space dimension , 2016 .

[3]  Waixiang Cao,et al.  Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations , 2014, Math. Comput..

[4]  Thorsten Gerber,et al.  Handbook Of Mathematical Functions , 2016 .

[5]  Chi-Wang,et al.  ANALYSIS OF SHARP SUPERCONVERGENCE OF LOCAL DISCONTINUOUS GALERKIN METHOD FOR ONE-DIMENSIONAL LINEAR PARABOLIC EQUATIONS , 2015 .

[6]  Hailiang Liu,et al.  A local discontinuous Galerkin method for the Burgers–Poisson equation , 2015, Numerische Mathematik.

[7]  Mahboub Baccouch,et al.  A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids , 2014, Comput. Math. Appl..

[8]  Feng Zhang,et al.  Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem , 2014, Journal of Scientific Computing.

[9]  Mahboub Baccouch,et al.  Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension , 2014, Comput. Math. Appl..

[10]  Mahboub Baccouch,et al.  Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems , 2014, Appl. Math. Comput..

[11]  Mahboub Baccouch,et al.  Adaptivity and Error Estimation for Discontinuous Galerkin Methods , 2014 .

[12]  Chi-Wang Shu,et al.  Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations , 2012, SIAM J. Numer. Anal..

[13]  Mahboub Baccouch,et al.  A Superconvergent Local Discontinuous Galerkin Method for Elliptic Problems , 2012, J. Sci. Comput..

[14]  Mahboub Baccouch,et al.  A local discontinuous Galerkin method for the second-order wave equation , 2012 .

[15]  Chi-Wang Shu,et al.  Discontinuous Galerkin Methods: Theory, Computation and Applications , 2011 .

[16]  Mahboub Baccouch,et al.  Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes , 2011 .

[17]  Chi-Wang Shu,et al.  Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension , 2010, SIAM J. Numer. Anal..

[18]  Zhimin Zhang,et al.  Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems , 2009, J. Sci. Comput..

[19]  Béatrice Rivière,et al.  Discontinuous Galerkin methods for solving elliptic and parabolic equations - theory and implementation , 2008, Frontiers in applied mathematics.

[20]  Chi-Wang Shu,et al.  Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations , 2007 .

[21]  Fatih Celiker,et al.  Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension , 2007, Math. Comput..

[22]  Paul Castillo,et al.  A review of the local discontinuous Galerkin (LDG) method applied to elliptic problems , 2006 .

[23]  Guido Kanschat,et al.  The local discontinuous Galerkin method for linearized incompressible fluid flow: a review , 2005 .

[24]  Guido Kanschat,et al.  A locally conservative LDG method for the incompressible Navier-Stokes equations , 2004, Math. Comput..

[25]  Slimane Adjerid,et al.  Superconvergence of Discontinuous Finite Element Solutions for Transient Convection–diffusion Problems , 2005, J. Sci. Comput..

[26]  Chi-Wang Shu,et al.  Error Estimates to Smooth Solutions of Runge-Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws , 2004, SIAM J. Numer. Anal..

[27]  Paul Castillo,et al.  A superconvergence result for discontinuous Galerkin methods applied to elliptic problems , 2003 .

[28]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[29]  Bernardo Cockburn,et al.  Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems , 2002, Math. Comput..

[30]  Ilaria Perugia,et al.  Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids , 2001, SIAM J. Numer. Anal..

[31]  Ilaria Perugia,et al.  An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems , 2000, SIAM J. Numer. Anal..

[32]  Dominik Schötzau,et al.  Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method , 2000, SIAM J. Numer. Anal..

[33]  Paul Castillo,et al.  An Optimal Estimate for the Local Discontinuous Galerkin Method , 2000 .

[34]  Chi-Wang Shu,et al.  The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems , 1998 .

[35]  Boleslaw K. Szymanski,et al.  Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws , 1997, J. Parallel Distributed Comput..

[36]  Karen Dragon Devine,et al.  Parallel adaptive hp -refinement techniques for conservation laws , 1996 .

[37]  Todd E. Peterson,et al.  A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation , 1991 .

[38]  S. Osher.  Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[39]  S. Adjerid,et al.  Superconvergence of the Local Discontinuous Galerkin Method Applied to Di usion Problems , 2022 .