Analysis and application of the IIPG method to quasilinear nonstationary convection-diffusion problems

Journal of Computational and Applied Mathematics

Volumn 222, Issue 2, 2008, Pages 251-273

  Dolejší, Vít ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Discontinuous Galerkin finite element method; Error estimates; Experimental order of convergence; Incomplete interior penalty Galerkin method; Method of lines; Quasilinear convection diffusion equation; Viscous compressible flows

Indexed keywords

DIFFUSION; DIFFUSION IN LIQUIDS; HEAT CONVECTION; LINEAR EQUATIONS; NUMERICAL METHODS; SEMICONDUCTOR DOPING;

DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD; ERROR ESTIMATES; EXPERIMENTAL ORDER OF CONVERGENCE; INCOMPLETE INTERIOR PENALTY GALERKIN METHOD; METHOD OF LINES; QUASILINEAR CONVECTION-DIFFUSION EQUATION; VISCOUS COMPRESSIBLE FLOWS;

ERROR ANALYSIS;

EID: 53449084618     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.10.055     Document Type: Article

References (28)

1. Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 4 (1982) 742-760
2. Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 5 (2002) 1749-1779
3. Babuška I., and Strouboulis T. The Finite Element Method and its Reliability (2001), Clarendon Press, Oxford
4. 2AN Math. Model. Numer. Anal. 21 (1987) 199-238
5. Babuška I., and Suri M. The p- and h-p versions of the finite element method. An overview. Comput. Methods Appl. Mech. Engrg. 80 (1990) 5-26
6. Ciarlet P.G. The Finite Elements Method for Elliptic Problems (1979), North-Holland, Amsterdam, New York, Oxford
7. Cockburn B. Discontinuous Galerkin methods for convection dominated problems. In: Barth T.J., and Deconinck H. (Eds). High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering vol. 9 (1999), Springer, Berlin 69-224
8. Discontinuous Galerkin methods. Theory computation and applications. In: Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds). 1st International Symposium on DGM. 24-26 May 1999, Newport, RI, USA. Lecture Notes in Computational Science and Engineering vol. 11 (2000), Springer, Berlin
9. Dawson C.N., Sun S., and Wheeler M.F. Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2565-2580
10. Dolejší V. Higher order semi-implicit discontinuous Galerkin finite element schemes for nonlinear convection-diffusion problems. In: de Castro A.B., Gómez D., Quintela P., and Salgado P. (Eds). Numerical Mathematics and Advanced Applications. ENUMATH, 2005 (2006), Springer-Verlag, Berlin, Heidelberg
11. V. Dolejší, Semi-implicit interior penalty discontinuous Galerkin methods for viscous compressible flows, Commun. Comput. Phys
12. 2)-error estimate of the discontinuous Galerkin method for a nonlinear nonstationary convection-diffusion problem, IMA J. Numer. Anal. Preprint No. MATH-knm-2007/1, Charles University Prague, School of Mathematics. www.karlin.mff.cuni.cz/ms-preprints, 2007
13. Dolejší V., Feistauer M., and Schwab C. A finite volume discontinuous Galerkin scheme for nonlinear convection-diffusion problems. Calcolo 39 (2002) 1-40
14. Dolejší V., Feistauer M., and Sobotíková V. A discontinuous Galerkin method for nonlinear convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 194 (2005) 2709-2733
15. M. Feistauer, On the finite element approximation of functions with noninteger derivatives, Numer. Funct. Anal. Optim. 10, 91-110
16. Feistauer M. Mathematical Methods in Fluid Dynamics (1993), Longman Scientific & Technical, Harlow
17. Feistauer M., Felcman J., and Straškraba I. Mathematical and Computational Methods for Compressible Flow (2003), Oxford University Press, Oxford
18. Feistauer M., and Ženísek A. Finite element solution of nonlinear elliptic problems. Numer. Math. 50 (1987) 451-475
19. Houston P., Robson J., and Süli E. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. IMA J. Numer. Anal. 25 (2005) 726-749
20. Houston P., Schwab C., and Süli E. Discontinuous h p-finite element methods for advection-diffusion problems. SIAM J. Numer. Anal. 39 6 (2002) 2133-2163
21. Rivière B., and Wheeler M.F. A discontinuous Galerkin method applied to nonlinear parabolic equations. In: Cockburn B., Karniadakis G.E., and Schu C.-W. (Eds). Discontinuous Galerkin Methods. Theory, Computation and Applications. Lect. Notes Comput. Sci. Eng. vol. 11 (2000), Springer, Berlin 231-244
22. Rivière B., Wheeler M.F., and Girault V. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. i. Comput. Geosci. 3 3-4 (1999) 337-360
23. Schwab C. p- and h p-Finite Element Methods (1998), Clarendon Press, Oxford
24. S. Sun, Discontinuous Galerkin methods for reactive transport in porous media, Ph.D. Thesis, The University of Texas, Austin, 2003
25. Sun S., and Wheeler M.F. Symmetric and nonsymmetric discontinuous Galerkin methods for reactive transport in porous media. SIAM J. Numer. Anal. 43 1 (2005) 195-219
26. Temam R. Navier-Stokes Equations. Theory and Numerical Analysis (1977), North-Holland, Amsterdam, New York, Oxford
27. Wesseling P. Principles of Computational Fluid Dynamics (2001), Springer, Berlin
28. Zeidler E. Nonlinear Functional Analysis and its Applications. II/B, Nonlinear Monotone Operators (1985), Springer, New York