On a family of discontinuous Galerkin fully-discrete schemes for the wave equation (original) (raw)
Adjerid S, Temimi H (2011) A discontinuous Galerkin method for the wave equation. Comput Methods Appl Mech Eng 200:837–849 ArticleMathSciNet Google Scholar
Arnold DN (1982) An interior penalty finite element method with discontinuous elements. SIAM J Numer Anal 19:742–760 ArticleMathSciNet Google Scholar
Arnold DN, Brezzi F, Cockburn B, Marini LD (2002) Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39:1749–1779 ArticleMathSciNet Google Scholar
Baker GA (1976) Error estimates for finite element methods for second-order hyperbolic equations. SIAM J Numer Anal 13:564–576 ArticleMathSciNet Google Scholar
Bassi F, Rebay S (1997) A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations. J Comput Phys 131:267–279 ArticleMathSciNet Google Scholar
Bassi F, Rebay S, Mariotti G, Pedinotti S, Savini M (1997) A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Decuypere R, Dibelius G (eds) Proceedings of 2nd European conference on turbomachinery, fluid dynamics and thermodynamics. Technologisch Instituut, Antwerpen, Belgium, 1997, pp 99–108
Bécache E, Joly P, Tsogka C (2000) An analysis of new mixed finite elements for the approximation of wave propagation problems. SIAM J Numer Anal 37:1053–1084 ArticleMathSciNet Google Scholar
Britt S, Tsynkov S, Turkel E (2018) Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials. J Comput Phys 354:26–42 ArticleMathSciNet Google Scholar
Brezzi F, Manzini G, Marini D, Pietra P, Russo A (1999) Discontinuous finite elements for diffusion problems, in Atti Convegno in onore di F. Brioschi (Milan, 1997), Istituto Lombardo, Accademia di Scienze e Lettere, Milan, Italy, 1999, pp 197–217
Castillo P, Cockburn B, Schötzau D, Schwab C (2002) Optimal a priori error estimates for the \(hp\)-version of the local discontinuous Galerkin method for convection-diffusion problems. Math Comput 71:455–478 ArticleMathSciNet Google Scholar
Cockburn B, Kanschat G, Schötzau D (2005) A locally conservative LDG method for the incompressible Navier-Stokes equations. Math Comput 74:1067–1095 ArticleMathSciNet Google Scholar
Cockburn B, Karniadakis GE, Shu C-W (2000) eds Discontinuous Galerkin methods. Theory, computation and applications, lecture notes in computer science engineering, vol 11. Springer, New York
Cockburn B, Shu C-W (1998) The local discontinuous Galerkin method for time-dependent convection–diffusion systems. SIAM J Numer Anal 35:2440–2463 ArticleMathSciNet Google Scholar
Cowsar LC, Dupont TF, Wheeler MF (1990) A-priori estimates for mixed finite element methods for the wave equations. Comput Methods Appl Mech Eng 82:205–222 ArticleMathSciNet Google Scholar
Diaz J, Grote MJ (2009) Energy conserving explicit local time stepping for second-order wave equations. SIAM J Sci Comput 31:1985–2014 ArticleMathSciNet Google Scholar
Douglas J Jr, Dupont T (1976) Interior penalty procedures for elliptic and parabolic Galerkin methods, vol 58. Lecture notes in physics. Springer, Berlin
French DA, Peterson TE (1996) A continuous space-time finite element method for the wave equation. Math Comput 65:491–506 ArticleMathSciNet Google Scholar
Gao H, Zhao H (2013) Analysis of a numerical solver for radiative transport equation. Math Comput 82:153–172 ArticleMathSciNet Google Scholar
Grote M, Schneebeli A, Schötzau D (2006) Discontinuous Galerkin finite element method for the wave equation. SIAM J Numer Anal 44:2408–2431 ArticleMathSciNet Google Scholar
Grote M, Schötzau D (2009) Optimal error estimates for the fully discrete interior penalty DG method for the wave equation. J Sci Comput 40:257–272 ArticleMathSciNet Google Scholar
Gustafsson B, Mossberg E (2004) Time compact high order difference methods for wave propagation. SIAM J Sci Comput 26:259–271 ArticleMathSciNet Google Scholar
Han W, He L, Wang F (2019) Optimal order error estimates for discontinuous Galerkin methods for the wave equation. J Sci Comput 78:121–144 ArticleMathSciNet Google Scholar
Han W, Huang J, Eichholz J (2010) Discrete-ordinate discontinuous Galerkin methods for solving the radiative transfer equation. SIAM J Sci Comput 32:477–497 ArticleMathSciNet Google Scholar
Han W, Reddy BD (2013) Plasticity: mathematical theory and numerical analysis, 2nd edn. Springer, Berlin Book Google Scholar
Han W, Sofonea M (2002) Quasistatic contact problems in viscoelasticity and viscoplasticity, studies in advanced mathematics, vol 30. Americal Mathematical Society, Providence, RI-International Press, Somerville, MA
Hu C, Shu C-W (1999) A discontinuous Galerkin finite element method for Hamilton–Jacobi equations. SIAM J Sci Comput 21:666–690 ArticleMathSciNet Google Scholar
Kornhuber R, Lepsky O, Hu C, Shu C-W (2000) The analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations. Appl Numer Math 33:423–434 ArticleMathSciNet Google Scholar
Kreiss HO, Petersson NA, Yström J (2002) Difference approximations for the second order wave equation. SIAM J Numer Anal 40:1940–1967 ArticleMathSciNet Google Scholar
Lions J-L, Magenes E (1972) Non-homogeneous boundary value problems and applications, vol I. Springer, New York Book Google Scholar
Walkington NJ (2014) Combined DG-CG time stepping for wave equations. SIAM J Numer Anal 52:1398–1417 ArticleMathSciNet Google Scholar
Wang F, Han W, Cheng X (2010) Discontinuous Galerkin methods for solving elliptic variational inequalities. SIAM J Numer Anal 48:708–733 ArticleMathSciNet Google Scholar
Wang F, Han W, Cheng X (2011) Discontinuous Galerkin methods for solving Signorini problem. IMA J Numer Anal 31:1754–1772 ArticleMathSciNet Google Scholar
Wang F, Han W, Cheng X (2014) Discontinuous Galerkin methods for solving a quasistatic contact problem. Numer Math 126:771–800 ArticleMathSciNet Google Scholar
Wang F, Zhang T, Han W (2019) \(C^{0}\) discontinuous Galerkin methods for a Kirchhoff plate contact problem. J Comput Math 37:184–200 ArticleMathSciNet Google Scholar