Improvements of the Mizukami-Hughes method for convection-diffusion equations

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 1-3, 2006, Pages 579-594

  Knobloch, Petr ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Convection diffusion; Convection diffusion reaction; Discrete maximum principle; Petrov Galerkin method; Stabilized FEM

Indexed keywords

DIFFUSION; FINITE ELEMENT METHOD; GALERKIN METHODS; MATHEMATICAL MODELS; PIECEWISE LINEAR TECHNIQUES; STEADY FLOW;

CONVECTION-DIFFUSION-REACTION; DISCRETE MAXIMUM PRINCIPLE; MIZUKAMI-HUGHES METHOD; PETROV-GALERKIN METHOD;

FLUID MECHANICS;

DIFFUSION; FINITE ELEMENT METHOD; FLUID MECHANICS; GALERKIN METHODS; MATHEMATICAL MODELS; PIECEWISE LINEAR TECHNIQUES; STEADY FLOW;

EID: 33846553061     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.06.004     Document Type: Article

References (16)

1. Almeida R.C., and Silva R.S. A stable Petrov-Galerkin method for convection-dominated problems. Comput. Methods Appl. Mech. Engrg. 140 (1997) 291-304
2. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
3. Burman E., and Ern A. Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3833-3855
4. Burman E., and Ern A. Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. Math. Comput. 74 (2005) 1637-1652
5. Burman E., and Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1437-1453
6. do Carmo E.G.D., and Alvarez G.B. A new upwind function in stabilized finite element formulations, using linear and quadratic elements for scalar convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2383-2402
7. Ciarlet P.G., and Raviart P.-A. Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Engrg. 2 (1973) 17-31
8. Codina R. A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation. Comput. Methods Appl. Mech. Engrg. 110 (1993) 325-342
9. Hughes T.J.R., Mallet M., and Mizukami A. A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput. Methods Appl. Mech. Engrg. 54 (1986) 341-355
10. Idelsohn S., Nigro N., Storti M., and Buscaglia G. A Petrov-Galerkin formulation for advection-reaction-diffusion problems. Comput. Methods Appl. Mech. Engrg. 136 (1996) 27-46
11. Ikeda T. Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena. Lecture Notes in Numerical and Applied Analysis vol. 4 (1983), North-Holland, Amsterdam
12. John V., Maubach J.M., and Tobiska L. Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Numer. Math. 78 (1997) 165-188
13. Knopp T., Lube G., and Rapin G. Stabilized finite element methods with shock capturing for advection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2997-3013
14. Mizukami A., and Hughes T.J.R. A Petrov-Galerkin finite element method for convection-dominated flows: an accurate upwinding technique for satisfying the maximum principle. Comput. Methods Appl. Mech. Engrg. 50 (1985) 181-193
15. Shih Y.-T., and Elman H.C. Modified streamline diffusion schemes for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 174 (1999) 137-151
16. Tezduyar T.E., and Park Y.J. Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput. Methods Appl. Mech. Engrg. 59 (1986) 307-325