1 |
J.S. Hesthaven, T.Warburton, Nodal Discontinuous Galerkin Methods: algorithms, analysis, and applications, Texts in Applied Mathematics, vol. 54, Springer Verlag, New York, USA, 2008.
|
2 |
M. Izadi, Streamline diffusion methods for treating the coupling equations of two hyperbolic conservation laws, Math. Comput. Model., 45 (2007), 201-214.
DOI
|
3 |
A. Vasseur, Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal., 160 (2001), 181-193.
DOI
|
4 |
S.N. Kruzkov, First order quasilinear equations in several independent variables, USSR Math. Sbornik. 10 (2) (1970) 217-243.
DOI
|
5 |
Adimurthi and G. D. V. Gowda, Conservation laws with discontinuous flux, J. Math. Kyoto Univ., 43 (2003), 27-70.
DOI
|
6 |
Y. Cheng, C.-W. Shu, 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), 4044-4072.
DOI
|
7 |
S. Osher, Riemann solvers, the entropy condition, and difference approximations, SIAM. J. Numer. Anal., 21 (1984), 217-235.
DOI
|
8 |
G. Jiang, C.-W. Shu, On a cell entropy inequality for discontinuous Galerkin methods, Math. Comput., 206 (1994), 531-538.
DOI
|
9 |
M. Izadi, A posteriori error estimates for the coupling equations of scalar conservation laws, BIT Numer. Math., 49(4) (2009), 697-720.
DOI
|
10 |
M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions, Dover, New York, 1965.
|
11 |
S. Bertoluzza, S. Falletta, G. Russo, and C.-W. Shu, Numerical Solution of Partial Differential Equations, in: Advanced Courses in Mathematics, CRM, Barcelona, 2008.
|
12 |
P.G. Ciarlet, The Finite Element Method for Elliptic Problems, Amesterdam, North Holland, 1987.
|
13 |
B. Cockburn, C.-W, Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput., 16 (2001), 173-261.
DOI
|
14 |
J.-M. Herard, Schemes to couple flows between free and porous medium, Proceedings of AIAA (2005), 2005-4861.
|
15 |
J.-M. Herard, O. Hurisse, Coupling two and one-dimensional unsteady Euler equations through a thin interface, Computer and Fluids, 36 (2007), 651-666.
DOI
|
16 |
E. Godlewski and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: I. the scalar case, Numer. Math., 97 (2004), 81-130.
DOI
|
17 |
E. Godlewski, K.-C. Le Thanh, P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The system case, M2AN Math. Model. Numer. Anal., 39 (2005), 649-692.
DOI
|
18 |
A. Ambroso, Ch. Chalons, F. Coquel, E. Godlewski, J.-M. Herard, F. Lagoutiere, P.-A. Raviart, and N. Seguin, The coupling of multiphase flow models, Proceedings of Nureth-11, Avignon, France, 2005.
|
19 |
A. Ambroso, Ch. Chalons, F. Coquel, E. Godlewski, J.-M. Herard, F. Lagoutiere, P.-A. Raviart, N. Seguin, and J.-M. Herard, Coupling of multiphase flow models, Proceedings of the 11th international meeting on nuclear thermohydraulics, Nureth, 2005.
|
20 |
A. Ambroso, Ch. Chalons, F. Coquel, E. Godlewski, J.-M. Herard, F. Lagoutiere, P.-A. Raviart, and N. Seguin, The coupling of homogeneous models for two-phase flows, Int. Journal for Finite Volume, 4 (2007), 1-39.
|
21 |
F. Coquel, Coupling of nonlinear hyperbolic systems: A journey from mathematical to numerical issues, in Vazquez-Cendon et al. (Eds.), Numerical Methods for Hyperbolic Equations, Taylor & Francis Group, London, (2013), 21-35.
|
22 |
B. Andreianov, K. H. Karlsen, and N. H. Risebro, A theory of -dissipative solvers for scalar conservation laws with discontinuous flux, Arch. Rational Mech. Anal., 201 (2011), 27-86.
DOI
|
23 |
R. Burger, K. H. Karlsen, Conservation laws with discontinuous flux: a short introduction, J. Engrg. Math., 60 (2008), 241-247.
DOI
|
24 |
R. Burger, K.H. Karlsen, J. Towers, On Enquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections, SIAM J. Numer. Anal., 3 (2009), 1684-1712.
|
25 |
S. Diehl, On scalar conservation laws with point source and discontinuous flux function, SIAM J. Math. Anal., 26 (1995), 1425-1451.
DOI
|
26 |
K. H. Karlsen, N. H. Risebro, and J. D. Towers, Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient, IMA J. Numer. Anal., 22(4) (2004), 623-664.
DOI
|
27 |
C. Johnson and J. Pitkaranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp., 46 (1986), 1-26.
DOI
|
28 |
K.H. Karlsen, N.H. Risebro, J. D. Towers, -stability for entropy solutions of nonlinear degenerate parabolic connection-diffusion equations with discontinuous coefficients, Skr.-K. Nor. Vidensk. Selsk. 3 (2003) 1-49.
|
29 |
W.H. Reed and T.R. Hill, Triangular mesh methods for the neutron transport equation, Tech. Report LA-UR- 73-479, Los Alamos Scientific Laboratory, Los Alamos, 1973.
|
30 |
P. LeSaint, and P. A. Raviart, On a finite element method for solving the neutron transport equation, In de Boor, C. (Eds.), Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, (1974), 89-145.
|
31 |
T. Peterson, A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation, SIAM. J. Numer. Anal., 28 (1991), 133-140.
DOI
|
32 |
G.R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp., 50 (1988), 75-88.
DOI
|
33 |
B. Cockburn, S. Hou, and C.W. Shu, The Runge-Kutta local projection discontinuous Galerkin method for conservation laws IV: the multidimensional case, Math. Comp., 54 (1990), 545-581.
DOI
|
34 |
C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), 439-471.
DOI
|
35 |
B. Cockburn, C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework, Math. Comp., 52 (1989), 411-435.
DOI
|
36 |
B. Cockburn, G.E. Karniadakis, and C. W. Shu (Eds.), Discontinuous Galerkin methods theory, computation and applications, Lecture Notes in Computational Science and Engineering, vol. 11, Springer, Berlin, 2000.
|
37 |
B. Cockburn, C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws V: Multidimensional systems, J. Comput. Phys.,141 (1998), 199-224.
DOI
|