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The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form.
C. A. A. Minoli, D. A. Kopriva, Discontinuous Galerkin spectral element approximations on moving meshes, J. Comput. Phys. 230 (2011) 1876–1902
1902
Earlier work this paper cites.
A. P. Lightman, W. H. Press, R. H. Price, S. A. Teukolsky, Problem book in relativity and gravitation, Princeton University Press, Princeton, NJ, 1975, available online at http://www.nr.com
1975
Earlier work this paper cites.
J. H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35 (1980) 48–56
1980
Earlier work this paper cites.
J. F. Thompson, Z. U. A. Warsi, C. W. Mastin, Numerical grid generation: Foundations and applications, North-Holland, New York, 1985, available online at http://www.erc.msstate.edu/publications/gridbook
1985
Earlier work this paper cites.
M. Shibata, T. Nakamura, Evolution of three-dimensional gravitational waves: Harmonic slicing case, Phys. Rev. D 52 (1995) 5428–5444
1995
Earlier work this paper cites.
M. H. Carpenter, D. Gottlieb, Spectral methods on arbitrary grids, J. Comput. Phys. 129 (1996) 74–86
1996
Earlier work this paper cites.
T. W. Baumgarte, S. L. Shapiro, Numerical integration of Einstein’s field equations, Phys. Rev. D 59 (1999) 024007
1999
Earlier work this paper cites.
J. Donea, A. Huerta, J.-P. Ponthot, A. Rodríguez-Ferran, Arbitrary Lagrangian-Eulerian Methods, in: E. Stein, R. de Borst, T. J. R. Hughes (Eds.), Encyclopedia of Computational Mechanics, Vol. 1, John Wiley & Sons, New York, 2004, Ch. 14
2004
Earlier work this paper cites.
M. A. Scheel, H. P. Pfeiffer, L. Lindblom, L. E. Kidder, O. Rinne, S. A. Teukolsky, Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74 (2006) 104006
2006
Earlier work this paper cites.
L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen, O. Rinne, A new generalized harmonic evolution system, Class. Quantum Grav. 23 (2006) S447–S462
2006
Cited alongside, same era.
D. A. Kopriva, Metric identities and the Discontinuous Galerkin spectral element method on curvilinear meshes, J. Sci. Comput. 26 (2006) 301–327
2006
Cited alongside, same era.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical recipes: The art of scientific computing, 3rd Edition, Cambridge University Press, Cambridge, UK, 2007
2007
Cited alongside, same era.
S. E. Field, J. S. Hesthaven, S. R. Lau, Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries, Class. Quantum Grav. 26 (2009) 165010
2009
Cited alongside, same era.
G. Zumbusch, Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime, Class.Quantum Grav. 26 (2009) 175011
D. A. Kopriva, G. Gassner, On the quadrature and weak form choices in collocation type Discontinuous Galerkin spectral element methods, J. Sci. Comput. 44 (2010) 136–155
2010
Later among the works it cites.
D. Radice, L. Rezzolla, Discontinuous Galerkin methods for general-relativistic hydrodynamics: Formulation and application to spherically symmetric spacetimes, Phys. Rev. D 84 (2011) 024010
2011
Later among the works it cites.
J. D. Brown, P. Diener, S. E. Field, J. S. Hesthaven, F. Herrmann, A. H. Mroué, O. Sarbach, E. Schnetter, M. Tiglio, M. Wagman, Numerical simulations with a first-order BSSN formulation of Einstein’s field equations, Phys. Rev. D 85 (2012) 084004
2012
Later among the works it cites.
L. Rezzolla, O. Zanotti, Relativistic hydrodynamics, Oxford University Press, Oxford, UK, 2013
2013
Later among the works it cites.
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2009
Cited alongside, same era.
D. A. Kopriva, Implementing spectral methods for partial differential equations, Springer Science+Business Media, New York, NY, 2009
2009
Cited alongside, same era.
S. E. Field, J. S. Hesthaven, S. R. Lau, A. H. Mroue, Discontinuous Galerkin method for the spherically reduced Baumgarte-Shapiro-Shibata-Nakamura system with second-order operators, Phys. Rev. D 82 (2010) 104051
2010
Cited alongside, same era.
T. W. Baumgarte, S. L. Shapiro, Numerical relativity: Solving Einstein’s equations on the computer, Cambridge University Press, Cambridge, UK, 2010
2010
Cited alongside, same era.
Cited in the paper.
Cited in the paper.
A. H. Mroué, M. A. Scheel, B. Szilágyi, H. P. Pfeiffer, M. Boyle, D. A. Hemberger, L. E. Kidder, G. Lovelace, S. Ossokine, N. W. Taylor, A. Zenginoğlu, L. T. Buchman, T. Chu, E. Foley, M. Giesler, R. Owen, S. A. Teukolsky, Catalog of 174 binary black hole simulations for gravitational wave astronomy, Phys. Rev. Lett. 111 (2013) 241104
2013
Later among the works it cites.
P. Mocz, M. Vogelsberger, D. Sijacki, R. Pakmor, L. Hernquist, A discontinuous Galerkin method for solving the fluid and magnetohydrodynamic equations in astrophysical simulations, Mon. Not. Roy. Astr. Soc. 437 (2014) 397–414
2014
Later among the works it cites.
O. Zanotti, M. Dumbser, A. Hidalgo, D. Balsara, An ADER-WENO finite volume AMR code for astrophysics, in: N. V. Pogorelov, E. Audit, G. P. Zank (Eds.), 8th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2013), Vol. 488 of Astronomical Society of the Pacific Conference Series, 2014, pp. 285–290
2014
Later among the works it cites.
E. Endeve, C. D. Hauck, Y. Xing, A. Mezzacappa, Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates, J. Comput. Phys. 287 (2015) 151–183
2015
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