Fetching the paper…
Reading the bibliography…
A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other discontinuities.
1903
Earlier work this paper cites.
H. E. Bell, The American Mathematical Monthly 72
1965
Earlier work this paper cites.
W. Reed and T. Hill, Conference: National topical meeting on mathematical models and computational techniques for analysis of nuclear systems, Ann Arbor, Michigan, USA, 8 Apr 1973 , Conference: National topical meeting on mathematical models and computational techniques for analysis of nuclear systems, Ann Arbor, Michigan, USA, 8 Apr 1973 LA-UR–73-479, CONF-730414–2 (1973)
1973
Earlier work this paper cites.
J. A. Scales, Geophysical Journal International 97
1989
Earlier work this paper cites.
G. B. Cook, Phys. Rev. D 50
1994
Earlier work this paper cites.
P. E. Buis and W. R. Dyksen, ACM Transactions on Mathematical Software (TOMS) 22
1996
Earlier work this paper cites.
S. Brandt and B. Brügmann, Physical Review Letters 78
1997
Earlier work this paper cites.
B. Cockburn and C.-W. Shu, J. Comput. Phys. 141
1998
Earlier work this paper cites.
B. Cockburn, in An introduction to the Discontinuous Galerkin method for convection-dominated problems; in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23–28, 1997 , Lecture Notes in Physics, edited by A. Quarteroni (Springer, Berlin, New York, 1998) pp. 150–268
1998
Earlier work this paper cites.
B. Cockburn, G. E. Karniadakis, and C.-W. Shu, in Discontinuous Galerkin Methods: Theory, Computation and Applications , Lecture Notes in Computational Science and Engineering, edited by B. Cockburn, G. E. Karniadakis, and C.-W. Shu (Springer, Berlin, New York, 2000) pp. 3–50
2000
Earlier work this paper cites.
G. Cook, Living Rev. Rel. 3
2000
Earlier work this paper cites.
Y. Notay, SIAM Journal on Scientific Computing 22
2000
Earlier work this paper cites.
W. Briggs, V. Henson, and S. McCormick, A Multigrid Tutorial: Second Edition (Society for Industrial and Applied Mathematics, 2000)
2000
Earlier work this paper cites.
B. Cockburn, J. Comput. Appl. Math. 128
2001
Earlier work this paper cites.
H. C. Elman, O. G. Ernst, and D. P. O’leary, SIAM Journal on scientific computing 23
2001
Earlier work this paper cites.
J. M. Melenk and B. I. Wohlmuth, Advances in Computational Mathematics 15
2001
Earlier work this paper cites.
S. Balay, K. Buschelman, W. D. Gropp, D. Kaushik, L. C. McInnes, and B. F. Smith, “PETSc home page,” (2001), http://www.mcs.anl.gov/petsc
2001
Earlier work this paper cites.
D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, SIAM Journal on Numerical Analysis 39
2002
Earlier work this paper cites.
Y. Saad, Iterative methods for sparse linear systems (Siam, 2003)
2003
Earlier work this paper cites.
G. B. Cook and H. P. Pfeiffer, Physical Review D 70
2004
Earlier work this paper cites.
M. Ansorg, B. Brügmann, and W. Tichy, Physical Review D 70
2004
Earlier work this paper cites.
H. P. Pfeiffer, J. Hyperbol. Differ. Eq. 2
2005
Earlier work this paper cites.
S. Sherwin, R. Kirby, J. Peiró, R. Taylor, and O. Zienkiewicz, International journal for numerical methods in engineering 65
2006
Earlier work this paper cites.
M. Caudill, G. B. Cook, J. D. Grigsby, and H. P. Pfeiffer, Physical Review D 74
2006
Earlier work this paper cites.
K. A. Dennison, T. W. Baumgarte, and H. P. Pfeiffer, Phys. Rev. D 74
2006
Earlier work this paper cites.
P. Houston, D. Schötzau, and T. P. Wihler, Mathematical Models and Methods in Applied Sciences 17
2007
Earlier work this paper cites.
T. W. Baumgarte, N. O’Murchadha, and H. P. Pfeiffer, Phys. Rev. D 75
2007
Cited alongside, same era.
M. Ansorg, Class. Quantum Grav. 24
2007
Cited alongside, same era.
J. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , Texts in Applied Mathematics (Springer, 2008)
2008
Cited alongside, same era.
R. S. Sampath, S. S. Adavani, H. Sundar, I. Lashuk, and G. Biros, in Proceedings of the 2008 ACM/IEEE conference on Supercomputing (IEEE Press, 2008) p. 18
2008
Cited alongside, same era.
P. Houston, E. Süli, and T. P. Wihler, IMA journal of numerical analysis 28
2008
Cited alongside, same era.
G. Lovelace, R. Owen, H. P. Pfeiffer, and T. Chu, Phys. Rev. D78
H. Sundar, G. Biros, C. Burstedde, J. Rudi, O. Ghattas, and G. Stadler, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (IEEE Computer Society Press, 2012) p. 43
2012
Later among the works it cites.
P. Ghysels, P. Kłosiewicz, and W. Vanroose, Numerical Linear Algebra with Applications 19
2012
Later among the works it cites.
P. Mocz, M. Vogelsberger, D. Sijacki, R. Pakmor, and L. Hernquist, Mon. Not. Roy. Astr. Soc. 437
2014
Later among the works it cites.
2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2008
Cited alongside, same era.
S. E. Field, J. S. Hesthaven, and S. R. Lau, Class. Quantum Grav. 26
2009
Cited alongside, same era.
G. Zumbusch, Class. Quantum Grav. 26
2009
Cited alongside, same era.
S. R. Lau, H. P. Pfeiffer, and J. S. Hesthaven, Commun. Comput. Phys. 6
2009
Cited alongside, same era.
Y. Shang, Computers & Mathematics with Applications 57
2009
Cited alongside, same era.
D. Schötzau and L. Zhu, Applied Numerical Mathematics 59
2009
Cited alongside, same era.
C. Lovadina and L. Marini, J. Sci. Comput. 40
2009
Cited alongside, same era.
2014
Later among the works it cites.
D. Schötzau, C. Schwab, T. Wihler, and M. Wirz, Exponential convergence of hp-DGFEM for elliptic problems in polyhedral domains (Springer, 2014)
2014
Later among the works it cites.
E. Endeve, C. D. Hauck, Y. Xing, and A. Mezzacappa, J. Comput. Phys. 287
2015
Later among the works it cites.
2015
Later among the works it cites.
O. Zanotti, F. Fambri, and M. Dumbser, Monthly Notices of the Royal Astronomical Society 452
2015
Later among the works it cites.
G. Mengaldo, D. De Grazia, D. Moxey, P. Vincent, and S. Sherwin, Journal of Computational Physics 299
2015
Later among the works it cites.
C. Bi, C. Wang, and Y. Lin, Computer Methods in Applied Mechanics and Engineering 297
2015
Later among the works it cites.
Y. Feng, M. Straka, T. Di Matteo, and R. Croft, (2015)
2015
Later among the works it cites.
S. A. Teukolsky, J. Comput. Phys. 312
2016
Later among the works it cites.
M. Bugner, T. Dietrich, S. Bernuzzi, A. Weyhausen, and B. Brügmann, Phys. Rev. D 94
2016
Later among the works it cites.
K. Henriksson, F. Foucart, L. E. Kidder, and S. A. Teukolsky, Class. Quantum Grav. 33
2016
Later among the works it cites.
A. Tsokaros, B. C. Mundim, F. Galeazzi, L. Rezzolla, and K. Uryū, Physical Review D 94
2016
Later among the works it cites.
J. M. Miller and E. Schnetter, Class. Quantum Grav. 34
2017
Later among the works it cites.
2017
Later among the works it cites.
2017
Later among the works it cites.
2018
Later among the works it cites.
F. Hébert, L. E. Kidder, and S. A. Teukolsky, Phys. Rev. D98
2018
Later among the works it cites.
M. Kronbichler and W. A. Wall, SIAM Journal on Scientific Computing 40
2018
Later among the works it cites.
J. E. Kozdon and L. C. Wilcox, Journal of Scientific Computing 76
2018
Later among the works it cites.
2019
Closest in time.
M. S. Fabien, M. G. Knepley, R. T. Mills, and B. M. Riviere, SIAM Journal on Scientific Computing 41
2019
Closest in time.