Streamline-diffusion F. E. M. for Sobolev equations with convection-dominated term

Applied Mathematics

Volumn 16, Issue 1, 2001, Pages 63-71

  Sun, Tongjun ^a  

^a South Campus of Shandong University ^*  (United States)

Author keywords

Convection dominated term; Sobolev equations; Streamline diffusion

Indexed keywords

EID: 84978984527     PISSN: 10051031     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11766-001-0038-7     Document Type: Article

References (14)

1. Johnson, C., Navert U., An analysis of some finite element methods for advection-dif fusion. In: O. Axelsson L. S. Frank and A. Van der Sluis. eds., Analytical and Numerical Approaches to Asymptotic Problems in Analysis. North-Holland. Amsterdam, 1981.
2. Johnson, C., Finite element methods for convection-diffusion problems, In R. Glowinski and J. L. lions, eds., Computing Methods In Engineering and Applied Sciences, V, North-Holland, Amsterdam, 1982.
3. Navert U., A finite element for convection-diffusion problems, Thesis, Chalmers Univ. of Technology, Goteborg, 1982.
4. Johnson, C., Navert, U. and Pitkaranta, J., Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg., 1985, 45:285-312.
5. Johnson, C. and Saranen, J., Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations, Math. Comp., 1986, 47:1-18.
6. Peter Hansbo and Anders Szepessy. A velocity-pressure streamline-diffusion finite element method for the incompressible Navier-Stokes equation. Comput. Methods Appl. Mech. Engrg., 1990, 84:175-192.
7. Sun Che, Zhang Yang and Wei Qiang, The streamline-diffusion F. E. analysis for convection-diffusion problems, Mathematica Numerics Sinica, 1996(3): 253-260.
8. Sun Che and Shen Hui. FDSD method for time-dependent convection-diffusion equations. Numer. Math. A Journal of Chinese University. English Series, 1998, 7(1):72-85.
9. Barenblatt, G. I., Zheltov, I. P., Kochina, I. N., Basic concepts in the theory of seepage of homogenous liquids in fissured rocks, J. Appl. Math.Mech., 1960, 24:1286-1303.
10. Chen, P. J., Gurtin M. E., On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys., 1968.19:614-627.
11. Davis, P. L., A quasilinear parabolic and a related third order problem, J. Math. Anal. Appl., 1970.49: 327-335.
12. Ewing, R. E., A coupled non-linear hyperbolic-Sobolev system, Ann. Mat. Pura Appl., Ser. IV, 1977, 114:331-349.
13. Ewing, R. E., Numerical solution of Sobolev partial differntial equations, SIAM J. Numer. Anal., 1975, 12:345-363.
14. Ewing, R. E., Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations, SIAM J. Numer. Anal., 1978.15:1125-1150.