Discontinuous Galerkin method for hyperbolic equations involving $$\delta $$-singularities: negative-order norm error estimates and applications

[1]  Chi-Wang Shu,et al.  Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data , 2014, Numerische Mathematik.

[2]  K. R Vijayakumar,et al.  Partial different equations , 2011 .

[3]  Jennifer K. Ryan,et al.  Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions , 2011, SIAM J. Sci. Comput..

[4]  Xiangxiong Zhang,et al.  On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes , 2010, J. Comput. Phys..

[5]  Jennifer K. Ryan,et al.  Local derivative post-processing for the discontinuous Galerkin method , 2009, J. Comput. Phys..

[6]  Robert Haimes,et al.  One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields , 2008, J. Sci. Comput..

[7]  Bernardo Cockburn,et al.  Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data , 2008, SIAM J. Numer. Anal..

[8]  C. Canuto,et al.  A Eulerian approach to the analysis of rendez-vous algorithms , 2008 .

[9]  Songming Hou,et al.  Solutions of Multi-dimensional Hyperbolic Systems of Conservation Laws by Square Entropy Condition Satisfying Discontinuous Galerkin Method , 2007, J. Sci. Comput..

[10]  Jennifer K. Ryan,et al.  On a One-Sided Post-Processing Technique for the Discontinuous Galerkin Methods , 2003 .

[11]  Endre Süli,et al.  Enhanced accuracy by post-processing for finite element methods for hyperbolic equations , 2003, Math. Comput..

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

[13]  Paula de Oliveira,et al.  On a Class of High Resolution Methods for Solving Hyperbolic Conservation Laws with Source Terms , 2002 .

[14]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[15]  A. Noussair,et al.  Analysis of nonlinear resonance in conservation laws with point sources and well-balanced scheme , 2000 .

[16]  A. Noussair,et al.  Analysis of Nonlinear Resonance in Conservation Laws with Point Sources and Well‐Balanced Scheme , 2000 .

[17]  P. de Oliveira,et al.  A converging finite volume scheme for hyperbolic conservation laws with source terms , 1999 .

[18]  Bernardo Cockburn,et al.  Discontinuous Galerkin Methods for Convection-Dominated Problems , 1999 .

[19]  Bernardo Cockburn.  An introduction to the Discontinuous Galerkin method for convection-dominated problems , 1998 .

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

[21]  J. Greenberg,et al.  Analysis and Approximation of Conservation Laws with Source Terms , 1997 .

[22]  Abdallah Chalabi,et al.  On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms , 1997, Math. Comput..

[23]  Ragnar Winther,et al.  Finite-difference schemes for scalar conservation laws with source terms. , 1996 .

[24]  Chi-Wang Shu,et al.  On a cell entropy inequality for discontinuous Galerkin methods , 1994 .

[25]  Barry Koren,et al.  A robust upwind discretization method for advection, diffusion and source terms , 1993 .

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

[27]  Randall J. LeVeque,et al.  A study of numerical methods for hyperbolic conservation laws with stiff source terms , 1990 .

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

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

[30]  A. H. Schatz,et al.  Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods , 1987 .

[31]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[32]  Claes Johnson,et al.  Finite element methods for linear hyperbolic problems , 1984 .

[33]  J. Bramble,et al.  Higher order local accuracy by averaging in the finite element method , 1977 .

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