A space-time discontinuous Galerkin method for linear convection-dominated Sobolev equations

Applied Mathematics and Computation

Volumn 210, Issue 2, 2009, Pages 490-503

  Sun, Tongjun ^a   Ma, Keying ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Discontinuous Galerkin method; Finite element method; Radau quadrature rule; Sobolev equations; Space time

Indexed keywords

GALERKIN METHODS;

APPROXIMATE SOLUTIONS; BASIS FUNCTIONS; CONVECTION-DOMINATED; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHOD; DISCRETE INTERVALS; EXISTENCE AND UNIQUENESS; NUMERICAL EXPERIMENTS; PRIORI ERROR ESTIMATES; RADAU QUADRATURE RULE; SOBOLEV EQUATIONS; SPACE-TIME; SPATIAL MESHES; THEORETICAL RESULTS; TIME STEPS; TIME-DISCONTINUOUS GALERKIN METHODS;

FINITE ELEMENT METHOD;

EID: 62949133348     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.01.020     Document Type: Article

References (18)

1. Eriksson K., Johnson C., and Thomé V. Time discretization of parabolic problems by the discontinuous Galerkin method. RAIAO, Anal. Numer. 19 (1985) 611-643
2. Eriksson K., and Johnson C. Adaptive finite element methods for parabolic problems I: a linear model problem. SIAM J. Numer. Anal. 28 (1991) 43-77
3. ∞. SIAM J. Numer. Anal. 32 (1995) 06-740
4. Eriksson K., and Johnson C. Adaptive finite element methods for parabolic problems IV: a nonlinear problem. SIAM J. Numer. Anal. 32 (1995) 1729-1749
5. Johnson C. Discontinuous Galerkin finite element methods for second order hyperbolic problems. Comput. Methods Appl. Mech. Eng. 107 (1993) 117-192
6. Karakashian O., and Makridaskis Ch. A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method. Math.Comput. 67 (1998) 479-499
7. Davis P.J., and Rabinowitz P. Methods of Numerical Integration (1975), Academic Press, New York
8. Barenblatt G.I., Zheltov I.P., and Kochina I.N. Basic concepts in the theory of seepage of homogenous liquids in fissured rocks. J. Appl. Math. Mech. 24 (1960) 1286-1303
9. Chen P.J., and Gurtin M.E. On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19 (1968) 614-627
10. Davis P.L. A quasilinear parabolic and a related third order problem. J. Math. Anal. Appl. 49 (1970) 327-335
11. Ewing R.E. A coupled nonlinear hyperbolic system. Ann. Math. Pura Appl., Ser. IV 114 (1977) 331-349
12. Ewing R.E. Numerical solution of Sobolev partial differential equations. SIAM J. Numer. Anal. 12 (1975) 345-363
13. Ewing R.E. Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations. SIAM J. Numer. Anal. 15 (1978) 1125-1150
14. Sun T. Streamline-diffusion F.E.M for Sobolev equation with convection dominated term. Appl. Math., J. Chinese University, English Series 16 (2001) 63-71
15. Sun T., and Yang D. The finite element difference streamline-diffusion methods for Sobolev equation with convection-dominated term. Appl. Math. Comput. 125 (2002) 325-345
16. Sun T., and Yang D. A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations. Appl. Math. Comput. 200 (2008) 147-159
17. Brenner S.C., and Scott L.R. The Mathematical Theory of Finite Element Methods (1994), Springer-Verlag, New York
18. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam