Analysis of an a posteriori error estimator for the transport equation with SN and discontinuous Galerkin discretizations

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

[2]  P. Raviart,et al.  On a Finite Element Method for Solving the Neutron Transport Equation , 1974 .

[3]  Juhani Pitkäranta.  Estimates for the Derivatives of Solutions to Weakly Singular Fredholm Integral Equations , 1980 .

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

[5]  G. Richter.  An Optimal-Order Error Estimate for the Discontinuous Galerkin Method , 1988 .

[6]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[7]  L. H. Howell,et al.  An adaptive mesh refinement algorithm for the discrete ordinates method , 1996 .

[8]  J. Oden,et al.  hp-Version discontinuous Galerkin methods for hyperbolic conservation laws , 1996 .

[9]  Slimane Adjerid,et al.  A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems , 2002 .

[10]  R. Baker.  A Block Adaptive Mesh Refinement Algorithm for the Neutral Particle Transport Equation , 2002 .

[11]  Christian Aussourd,et al.  Styx: A Multidimensional AMR SN Scheme , 2003 .

[12]  G. Rimpault,et al.  ERANOS 2.1 : International Code System for GEN IV Fast Reactor Analysis , 2006 .

[13]  Yousry Y. Azmy,et al.  Error Comparison of Diamond Difference, Nodal, and Characteristic Methods for Solving Multidimensional Transport Problems with the Discrete Ordinates Approximation , 2007 .

[14]  Bo Dong,et al.  Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes , 2008, SIAM J. Numer. Anal..

[15]  Ludmil Zikatanov,et al.  A posteriori error estimator and AMR for discrete ordinates nodal transport methods , 2009 .

[16]  L. Gastaldo,et al.  HIGH-ORDER DISCRETE ORDINATE TRANSPORT IN NON-CONFORMING 2D CARTESIAN MESHES , 2009 .

[17]  Jean C. Ragusa,et al.  A two-mesh adaptive mesh refinement technique for SN neutral-particle transport using a higher-order DGFEM , 2010, J. Comput. Appl. Math..

[18]  Damien Fournier,et al.  High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS , 2010 .