On the performance of SOLD methods for convection–diffusion problems with interior layers

International Journal of Computing Science and Mathematics

Volumn 1, Issue 2-4, 2007, Pages 245-258

  John, V ^a   Knobloch, P ^b  

^a SAARLAND UNIVERSITY   (Germany)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

convection diffusion equations; interior layers; spurious oscillations at layers diminishing (SOLD) methods; streamline upwind Petrov Galerkin (SUPG) method

Indexed keywords

EID: 40249091515     PISSN: 17525055     EISSN: 17525063     Source Type: Journal    
DOI: 10.1504/ijcsm.2007.016534     Document Type: Article

References (15)

1. Brooks, A.N. and Hughes, T.J.R. (1982) ‘Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations’, Comput. Methods Appl. Mech. Eng., Vol. 32, pp.199–259.
2. Burman, E. and Ern, A. (2002) ‘Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation’, Comput. Methods Appl. Mech. Eng., Vol. 191, pp.3833–3855.
3. Burman, E. and Ern, A. (2005) ‘Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence’, Math. Comput., Vol. 74, pp.1637–1652.
4. Ciarlet, P.G. (1991) ‘Basic error estimates for elliptic problems’, in Ciarlet, P.G. and Lions, J.L. (Eds.): Handbook of Numerical Analysis, Vol. 2 – Finite Element Methods (pt. 1), North Holland, Amsterdam, pp.17–351.
5. Codina, R. (1993) ‘A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation’, Comput. Methods Appl. Mech. Eng., Vol. 110, pp.325–342.
6. do Carmo, E.G.D. and Galeão, A.C. (1991) ‘Feedback Petrov-Galerkin methods for convection-dominated problems’, Comput. Methods Appl. Mech. Eng., Vol. 88, pp.1–16.
7. Dolejši, V. (1998) ‘Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes’, Comput. Visual. Sci., Vol. 1, pp.165–178.
8. Hughes, T.J.R., Franca, L.P. and Hulbert, G.M. (1989) ‘A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations’, Comput. Methods Appl. Mech. Eng., Vol. 73, pp.173–189.
9. John, V. and Knobloch, P. (2007) ‘On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: part I – a review’, Comput. Methods Appl. Mech. Eng., Vol. 196, pp.2197–2215.
10. John, V. and Matthies, G. (2004) ‘MooNMD – a program package based on mapped finite element methods’, Comput. Visual. Sci., Vol. 6, pp.163–170.
11. Knobloch, P. (2006) ‘Improvements of the Mizukami-Hughes method for convection-diffusion equations’, Comput. Methods Appl. Mech. Eng., Vol. 196, pp.579–594.
12. Knopp, T., Lube, G. and Rapin, G. (2002) ‘Stabilized finite element methods with shock capturing for advection-diffusion problems’, Comput. Methods Appl. Mech. Eng., Vol. 191, pp.2997–3013.
13. Mizukami, A. and Hughes, T.J.R. (1985) ‘A Petrov-Galerkin finite element method for convection-dominated flows: an accurate upwinding technique for satisfying the maximum principle’, Comput. Methods Appl. Mech. Eng., Vol. 50, pp.181–193.
14. Roos, H-G., Stynes, M. and Tobiska, L. (1996) Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems, Springer-Verlag, Berlin.
15. Tabata, M. (1977) ‘A finite element approximation corresponding to the upwind finite differencing’, Mem. Numer. Math., Vol. 4, pp.47–63.