A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation

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

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

[3]  Yulong Xing,et al.  Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation , 2014, J. Comput. Appl. Math..

[4]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[5]  Ohannes A. Karakashian,et al.  Piecewise solenoidal vector fields and the Stokes problem , 1990 .

[6]  Chi-Wang Shu,et al.  Superconvergence and time evolution of discontinuous Galerkin finite element solutions , 2008, J. Comput. Phys..

[7]  Chi-Wang Shu,et al.  The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V , 1998 .

[8]  Felipe Linares,et al.  Scaling, stability and singularities for nonlinear, dispersive wave equations: the critical case , 2002 .

[9]  Yan Xu,et al.  Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations , 2012, SIAM J. Numer. Anal..

[10]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[11]  Chi-Wang Shu,et al.  A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives , 2007, Math. Comput..

[12]  Chi-Wang Shu,et al.  TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .

[13]  Chi-Wang Shu,et al.  The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .

[14]  Ohannes A. Karakashian,et al.  Convergence of Galerkin Approximations for the Korteweg-de Vries Equation, , 1983 .

[15]  T. Benjamin.  The stability of solitary waves , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  Charalambos Makridakis,et al.  A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation , 2014, Math. Comput..

[17]  Chi-Wang Shu,et al.  Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments , 2014 .

[18]  Chi-Wang Shu,et al.  TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems , 1989 .

[19]  Ohannes A. Karakashian,et al.  On some high-order accurate fully discrete Galerkin methods for the Korteweg-de Vries equation , 1985 .

[20]  Frank Merle,et al.  Existence of blow-up solutions in the energy space for the critical generalized KdV equation , 2001 .

[21]  J. Bona.  On the stability theory of solitary waves , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[22]  Frank Merle,et al.  Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation , 2002 .

[23]  Yulong Xing,et al.  Conservative, discontinuous Galerkin-methods for the generalized Korteweg-de Vries equation , 2013, Math. Comput..

[24]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[25]  Chi-Wang Shu,et al.  Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..

[26]  Ricardo H. Nochetto,et al.  A posteriori error estimates for the Crank-Nicolson method for parabolic equations , 2005, Math. Comput..